Ms Sturgeon tweeted she had been experiencing mild symptoms on Friday evening.
She will work from home over the next few days and told followers she would “hopefully” be back out and about later next week.
The First Minister met Sinn Fein vice president and first minister designate of Northern Ireland, Michelle O’Neill, at Bute House earlier on Friday.
She also travelled to the US earlier in the week where she met the Speaker of the House of Representatives, Nancy Pelosi, and addressed the Brookings Institute in Washington DC.
SNP colleagues including Westminster leader Ian Blackford sent get-well wishes.
MP for Glasgow North East Anne McLaughlin and Minister for Women’s Health Maree Todd wished her a speedy recovery.
Ms McLaughlin said: “This is just to get out of making me coffee, isn’t it?”
Ms O’Neill tested negative for Covid-19 later on Friday.
A Sinn Fein spokesperson said: “Michelle O’Neill has tested negative for Covid-19 this evening following her meeting with Nicola Sturgeon today, but will also be testing tomorrow as a precaution.”
Ms Sturgeon’s positive infection comes as Covid cases in Scotland continue to fall. The Office for National Statistics estimated 122,000 people had Covid in the week ending May 13.
It is the eighth weekly consecutive drop and the lowest number of cases since before Christmas when cases rose due to the Omicron variant spreading.
Public health restrictions such as social distancing and wearing face masks have been lifted and as of May 1 guidance for those experiencing symptoms of Covid was to stay at home.
For those too unwell to do “normal activities”, the advice is to stay at home until they feel better.
Scotland’s largest health board NHS Greater Glasgow and Clyde confirmed they would lift Covid restrictions on Friday.
As of Monday May 23, patients will be allowed a maximum of two interchangeable visitors and social distancing will be scrapped.