New figures seen exclusively by The Scotsman show 6,734 people had been pinged by the Protect Scotland app, run by NHS Scotland's Test and Protect, for the month to July 15.
It is a rise on the 5,780 people told to self-isolate in June, and the 913 ordered to do so in May.
The July data is also the highest figure recorded since December, and is on course to set a monthly record for close contacts alerted by the app over a period extending back to September last year.
The figures can be released as Nicola Sturgeon warned talk of Freedom Day was “not sensible”, with almost 1,800 new coronavirus cases recorded in the 24 hours to yesterday as Scotland moves to level zero restrictions today.
Despite the jump in figures, the result is a huge contrast to numbers outside Scotland, with 500,000 people pinged by the NHS app south of the border in a week.
The Protect Scotland app had been downloaded a total of 2,050,880 million times as of July 15.
Scottish Conservative shadow cabinet health secretary Annie Wells said: “We must all remain vigilant as record numbers of people are now being told to self-isolate.
“However, the SNP Government app does not appear to be performing as strongly as elsewhere in the UK. That is especially troubling considering Scotland was the Covid capital of Europe only a few weeks ago.
“It should be a real cause for concern that the Test and Protect system in Scotland has been struggling to cope with increased volumes in recent weeks, even though the app is not reaching as many people as it perhaps should.”
Liberal Democrat Health spokesperson Alex Cole-Hamilton MSP warned Test and Protect was “struggling to keep up” with the virus.
He said: "Now that the vaccine is helping us to turn the tide against the virus, the Scottish Government should put in place a test and release system to allow those who are pinged by the app, but test negative to go about their business.
"The Scottish Government also needs to make it far easier for people who are isolating to access financial support. That would mean people would be less likely to push the limits of the system.
"In the meantime, I would urge everyone who can to get their jab and to keep the app installed. We can only defeat this virus if we are all careful and observing the possibly life-saving measures."
Read more: What Covid rules will change on 19 July?
The highest figure was recorded by the Protect Scotland app in October last year, with 10,007 people told to self-isolate.
Numbers then steadily fell before plummeting to below 1,000 in April of this year.
Responding to the figures, the Scottish Government insisted the app was working “effectively”.
A spokesperson said: “As of July 14, 2021, the total number of people who have downloaded the Protect Scotland app is 2,052,012 with the number of contact notifications at 57,550.
“We’re confident the app is working effectively – and it is playing an essential role in the Test and Protect system to help suppress virus transmission.
“Updates to improve the app still further are made whenever possible based on feedback from officials and app users.
“The success of the app is also dependent on people uploading a test result code when they have a positive test and we would encourage as many people as possible to do this.”
Last week Scottish health secretary Humza Yousaf admitted Test and Protect was still not meeting international standards, but insisted it would improve.
Opposition parties have warned the system had “cut corners” to improve turnaround times and was not working properly.
It comes asfigures showed 1,735 new cases of Covid-19 were reported in the 24 hours to yesterday in Scotland, with 46 people in intensive care and 511 in hospital on Saturday.
There were no new reported deaths of people who had tested positive for the virus, according to Sunday’s figures, but the government noted register offices were generally closed at weekends.
The overall death toll, under the measure of people who first tested positive for the virus within the previous 28 days, remains at 7,800.
In response to the statistics, Ms Sturgeon said talk of ‘Freedom Day’, as it has been dubbed in England, was “not sensible” given the high daily numbers.
Ms Sturgeon tweeted: “As this chart shows, cases in (Scotland) are falling, but still too high.
“To talk of tomorrow as ‘freedom day’ (England only remember) is not sensible IMO, given current situation.
“Vaccines going well and do offer route through – but as we vaccinate, we must ease up gradually.
"If you live in or visiting (Scotland) please abide by remaining safety measures.
“Stick to group limits, keep 1m distance in public places, wear face masks, wash hands etc.
“While we vaccinate, these measures help keep us safe.”
All of Scotland will be in level zero from today, seeing a raft of measures scrapped on the same day England removes all remaining restrictions.
However, rules will continue to apply, including the mandatory wearing of face coverings.
It comes with almost a third of younger adults in Scotland still being unvaccinated despite all over-18s being offered a first dose vaccine appointment.
The most recent figures from Public Health Scotland showed that 31.6 per cent had still not had their first dose of a vaccine.
This suggests more than 260,000 younger adults have no protection at all, with only a fifth of this age group having had both doses.
National clinical director Professor Jason Leitch explained earlier this month that uptake of the vaccine among 18 to 29-year-olds had been slower than for other age groups.
Mr Yousaf said everyone who had taken up their offer of a vaccine was "playing their part in helping us out of the pandemic".
He said: "All of the evidence says that the vaccines are working as we continue to battle the faster-transmitting Delta variant, which is now dominant, so I urge everyone to take advantage of the vaccination programme which is open to every adult in Scotland.
"We have made getting a vaccination easier than ever – head to one of the drop-in clinics being offered across the country or, if you prefer, book an appointment online at NHS Inform."
A total of 2,390,353 people in Scotland have now been tested for coronavirus since the start of the outbreak, with the number confirmed as positive at 329,387.
Office for National Statistics (ONS) figures suggest around one in 90 people in Scotland are estimated to have had Covid-19 in the week to July 10.
The figure is up from one in 100 in the previous week and the highest level since the ONS infection survey began in Scotland at the end of October.
Overall, 3,976,022 people have now received the first dose of the vaccination and 2,966,054 have had their second dose.