Photographs of Calderwood visiting her holiday home in Earlsferry, on Scotland’s east coast about an hour’s drive from the capital Edinburgh, were published in the Scottish Sun.
Calderwood had apologised earlier on Sunday when she appeared next to Sturgeon at a news briefing that was supposed to update the country on the response to the pandemic, but was instead dominated by her actions.
“I did not follow the advice I’m giving to others, I’m truly sorry for that,” she said.
She said she had seen comments calling her a hypocrite and saying she was irresponsible.
“What I did was wrong. I’m very sorry,” she said.
She also apologised to police and National Health Service (NHS) colleagues.
But the apology did little to calm a storm of criticism from opposition politicians and the public.
Police Scotland said officers had spoken to Calderwood about her actions and had warned her about her future conduct.
“The legal instructions on not leaving your home without a reasonable excuse apply to everyone,” Chief Constable Iain Livingstone said in a statement.
“Individuals must not make personal exemptions bespoke to their own circumstances. It is vital everyone adheres to these requirements.”
Sturgeon had said earlier on Sunday that the chief medical officer would no longer take part in coronavirus media briefings, and that she had not known Calderwood was spending weekends at her second home.
“I am acutely aware of the importance of public trust in the advice the government is giving to stay at home in order to save lives and protect our NHS,” Sturgeon said.
Scotland has recorded 3345 coronavirus cases and 218 deaths.