Confirming the decision earlier today (28 May), First Minister Nicola Sturgeon said she had hoped to ease the curbs this week, but advisers felt the move would be 'premature'.
However, she added that Glasgow could move down to Level 2 from next Saturday (5 June), with a decision due on Wednesday (2 June).
Sturgeon said: "There are some early signs that the situation is stabilising in Glasgow.
"Weighing up all of these different factors is inevitably really difficult - case numbers in Glasgow are uncomfortably high, but we are seeing signs of progress.
"The view of the national incident management team is two-fold.
"Firstly, that it would be premature to move Glasgow out of level three immediately this week while the situation remains so fragile.
"However, and secondly, if incidence continues to stabilise and assuming levels of hospitalisation remain reasonably stable, the incident management team has made clear to me that they would support a move to level two from the end of next week."
Under Level 3 of Scotland's five-tier system of Coronavirus restrictions, alcohol sales are restricted to outdoor settings and hospitality businesses are subject to a 10pm curfew.
Indoor service is limited to the sale of food and non-alcoholic drinks for groups of up to four people from no more than two households, and subject to an 8pm curfew.
The rest of mainland Scotland currently remains in Level 2, with pubs and restaurants able to serve alcohol indoors to groups of up to six adults from three households, subject to a 10:30pm curfew.
Sturgeon added that a decision on whether the rest of Scotland would be able to move to Level 1 on 7 June, as planned, would also be made next week.
Under Level 1 restrictions, hospitality is only subject to an 11pm curfew and able to host groups of up to eight people from three households indoors.
Reacting to the decision to hold Glasgow in Level 3 for another week, UKHospitality Scotland's executive director, Leon Thompson, said: “Today’s news is a bitter blow for hospitality businesses.
"UKHospitality Scotland members in Glasgow are experiencing devastating financial burdens with owners, operators and workers struggling with the pressure of this ongoing situation. Waiting another week in the hope of good news will sap morale further, heaping more misery on businesses that have not been able to trade fully since last October.
"It is essential that the Scottish Government fully recognises the devastation being caused to Glasgow’s most important business sector and provides the necessary financial support to hospitality businesses, to avoid closures and job losses.”
Affected businesses in Glasgow are entitled to a grant worth up to £750 for each week the restrictions are extended.
"With the vaccine roll-out and all the preventative measures that the government has had us put in place, it should be possible to remove Glasgow from these unfair restrictions now," said Stephen Montgomery, spokesperson for the Scottish Hospitality Group and owner of Townhead Hotel in Lockerbie.
"Here we have a situation where Scottish Government thinks that keeping Glasgow City in Level 3 and throwing hospitality businesses a pitiful £750 per week is acceptable."