The Scottish First Minister said she did the "girl job of running the country" while her husband did the cooking and cleaning.
Appearing with her husband Philip on the BBC's The One Show, Ms May said there are specific "boy jobs and girl jobs" around the house, prompting allegations of sexism.
When asked if the same rules applied in her house, Ms Sturgeon told ITV's Peston on Sunday programme: “I’m afraid in my household my husband does all the cooking and most of the domestic tasks.
“I get on with the girl job of running the country.”
She added: "I don't want to get into a ding-dong with the Prime Minister here but I think it's really important, we're all trying to break down gender stereotypes and I've spent a lot of time, and I know Theresa May will agree with this, saying to girls there's nothing off limits, you should aspire to whatever you want to do.
"I think we've got to be careful that we don't then just play into these gender stereotypes."
The SNP leader also said she thought the Prime Minister was "feart" to join her to take part in televised General Election debates such as ITV Leader's Debate on Thursday night.
"Theresa May seems to want to go through this election dodging the public, dodging any real questions.
"So I'll challenge her today, change your mind, come and join us on Thursday - I'd say the same to Jeremy Corbyn - and let's have a proper debate."
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