Latest data shows there are 58.3 Covid-19 infections per 100,000 population and a senior health official has warned there were clusters of high infection rates in parts of the city.
It comes as all mainland local authority areas, except Moray, are due to move to level two of the routemap out of lockdown on Monday.
The First Minister tweeted: “We are seeing an increase in cases in Glasgow just now and, amidst concern about the so-called Indian variant, we are monitoring it very closely.”
It followed comments from Linda de Caestecker, director of public health at NHS Greater Glasgow and Clyde, that an increase in case numbers was to be expected as restrictions eased but she was “concerned” about a rise in Glasgow.
She told Radio Scotland: “The numbers go up very, very quickly – particularly as we see new variants coming in that are more transmissible.
“What we know is that it’s not the Kent variant, so the assumption is it’s the Indian variant, but we haven’t got the sequencing yet so we can’t be sure.”
Meanwhile, weekly deaths from Covid-19 in Scotland have fallen to single figures for the first time since September last year, according to the latest data.
Newly published National Records of Scotland (NRS) figures show seven deaths related to coronavirus were registered between May 3 and May 9, down 12 on the previous week.
It is the lowest total recorded in almost eight months.
Deaths from the virus have been steadily falling since around mid-January, when they hit 452 during the second winter peak.
They were last in single figures in the week beginning September 7, when five deaths were recorded.
The latest data shows 10,104 people have now died with coronavirus in Scotland since the pandemic began.
In the most recent week, North Lanarkshire recorded two coronavirus-related deaths, and Angus, Glasgow, Inverclyde, Midlothian and South Lanarkshire all recorded one.
Five deaths occurred in hospitals, one took place in a care home and one in a non-institutional setting such as at home.
Pete Whitehouse, director of statistical services at NRS, said: “There were seven registered Covid-related deaths last week which is the lowest number since September 2020.
“Across Scotland there were no registered Covid-related deaths in 26 of the 32 local authority areas.
“The total deaths from all causes were 12% below the average level for this time of year, although last week included a public holiday and some death registration may have been delayed.”
The NRS statistics are published each week and cover all deaths registered in Scotland where Covid-19 is mentioned on the death certificate.
They differ from the lab-confirmed coronavirus deaths announced daily by the Scottish Government because the NRS figures include suspected or probable cases of Covid-19.
Under the daily measure, 345 new cases of coronavirus were recorded in the past 24 hours, and no deaths.