The Prime Minister's intervention comes amid growing controversy over the appointment of Mr Young to the universities regulator, the Office for Students.
The writer and free schools pioneer has faced calls to quit after a string of crude and sexist comments on social media surfaced.
He has been backed by the likes of Cabinet ministers Boris Johnson and Michael Gove, but senior Labour MPs have called on Mrs May to act over his "virulent misogyny".
When asked about Mr Young on the BBC's Andrew Marr Show, the PM said: "Toby Young has done exceedingly good work in relation to free schools and that's what has led to him being appointed to the Office for Students.
"When he was appointed I was not aware of these comments that he had made. Frankly I'm not at all impressed by those comments.
"He's now in public office and as far as I'm concerned if he was to continue to use that sort of language and talk in that sort of way he would no longer be in public office."
Mr Young was named as a board member on the new watchdog by Mr Johnson's brother, Universities Minister Jo Johnson, on Monday.
His previous posts include a 2012 tweet when he wrote watching Prime Minister's Questions: "Serious cleavage behind Ed Miliband's head. Anyone know who it belongs to?"
A 2009 post read: "What happened to Winkleman's breasts (sic) Put on some weight, girlie #comicrelief."
Mr Young said earlier this week that he regretted the "sophomoric, politically incorrect remarks", adding: "I hope people will judge me on my actions."
There were more headlines about Mr Young in Sunday's newspapers, with the Mail on Sunday reporting that his social media comments included a sexual "joke" about starving children on Comic Relief.
Mr Young told the paper that he had been a "provocative journalist" for three decades and part of that was saying "controversial, sometimes outrageous things" and that it was not surprising people were able to find material to embarrass him.
He said all of the offensive messages were at least five years old and most much older, and that he was a changed man now, adding: "I'm a more serious person now."
Sir Vince Cable said Mr Young's appointment was "completely unsustainable".
"This is a man who has a record of misogyny and backs eugenics, screening out people of supposedly low intelligence," the Lib Dem leader said.
"This shows bad judgement and, as the Prime Minister effectively admitted, a lack of due diligence. It seems all you need to survive is be a friend of Boris Johnson."