Sturgeon, who is Scotland’s first female First Minister, tweeted a photograph of herself with May on the steps of Bute House on Friday.
She wrote: “Politics aside – I hope girls everywhere look at this photograph and believe nothing should be off limits for them.”
May, who was appointed Prime Minister on Wednesday, is only the second woman to hold the title after Margaret Thatcher.
Sturgeon has said the Brexit vote could lead to another independence referendum - as the majority of Scots voted to remain a member of the EU.
With Scotland voting 62% to 38% to remain in the EU at the Brexit referendum, Sturgeon has warned it would be against the country’s national interest to be forced out of the bloc by pro-withdrawal majorities in England and Wales.
But May said: “I think the question is: should there be another referendum?”
“As far as I’m concerned the Scottish people had their vote, they voted in 2014, and a very clear message came through, both the United Kingdom and the Scottish Government said they would abide by that.”