The decision was taken to keep Scotland’s biggest city under Level 3 restrictions while the rest of the country – excluding Moray, which was then also moved down – went to Level 2 earlier this month.
On Sunday, the Greater Glasgow and Clyde health board area reported a seven-day case rate per 100,000 people of 95.7, more than double the Scottish average of 42.5.
A decision on whether the city will also be able to see restrictions ease is expected later this week but Humza Yousaf said this week would be “critical”.
“There’s a range of data we look at,” the Health Secretary said.
“We obviously want to see those cases per 100,000 falling, we obviously want to see the test positivity falling, we want to look at hospital admissions and also ICU admissions – I think that’s quite critical and quite key.
“But also what I want to hear from local public health directors is can they contain it? Can it be managed?”
He added: “The last thing we want to do is if we’re not quite sure, move Glasgow down a level only for in the weeks and months to come then we have to increase the level again and put them back into Level 3.
“That yo-yoing effect isn’t going to help anybody at all.
“I don’t want to keep anybody in any level or any restriction for a minute longer than we have to but this week is going to be quite critical when we look at the data.”
While he said the data this week would be key, Mr Yousaf said he was “reticent” to say ahead of time what the data would need to show for Glasgow to be able to move into Level 2.
Clackmannanshire has also seen a major spike in cases, with the rate per 100,000 in the week up to May 20 at 126.1.
However, the Health Secretary said this could be due to the relatively low population in the council area.
“Clackmannanshire has a really small population, so even four, five, six households testing positive can really make the numbers look like they’re shooting up,” he said.
“But it is a concerning situation, I’m not going to lie to you about that – it’s one of the local authorities we’re looking at and speaking to local health directors, can it be contained and can it be managed?
“But Clackmannanshire is one of the local authorities that’s giving us a little bit of concern.”