The Scottish Sun has published a photograph of Nicola Sturgeon standing talking to three people at a social distance, but with her face uncovered.
She was attending a wake after the funeral of a Scottish government civil servant who died with Covid.
Ms Sturgeon had been wearing a tartan mask and is said to have taken it off briefly as she was leaving the venue.
The Scottish government's Covid regulations say that customers in hospitality venues must wear a face covering except when seated - including when they are entering, exiting and moving around.
Anyone who breaches the face covering rules can be punished by a fixed penalty notice of £60.
In a statement released to the BBC, the first minister said: "Last Friday, while attending a funeral wake, I had my mask off briefly.
"This was a stupid mistake and I'm really sorry. "I talk every day about the importance of masks, so I'm not going to offer any excuses.
"I was in the wrong, I'm kicking myself, and I'm sorry."
Ms Sturgeon is understood to have been at the wake in the Stable Bar and Restaurant in Edinburgh after attending a service at nearby Mortonhall Crematorium.
The first minister regularly use her daily coronavirus briefings to remind people to cover their faces to limit the risk of spreading the virus.
A Scottish Conservative spokesman said: "The first minister should know better. By forgetting the rules and failing to set a proper example, she's undermining essential public health messaging.
"It's a blunder that an ordinary member of the public wouldn't get away with. There cannot be one rule for Nicola Sturgeon and another for everyone else."
A truly rich man is one whose children run into his arms when his hands are empty.