The US president had earlier retweeted three inflammatory videos posted online by a British far-right group.
Mrs May's spokesman said it was "wrong for the president to have done this".
The US and the UK are close allies and often described as having a "special relationship". Theresa May was the first foreign leader to visit the Trump White House.
.@Theresa_May, don’t focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. We are doing just fine!— Donald J. Trump (@realDonaldTrump) November 30, 2017
In hitting out at Mrs May, Mr Trump first tagged the wrong Twitter account, sending his statement to a different user with just six followers. He then deleted the tweet and posted it again, this time directing the message to the UK PM's official account.VIDEO: Islamist mob pushes teenage boy off roof and beats him to death! pic.twitter.com/XxtlxNNSiP— Jayda Fransen (@JaydaBF) November 29, 2017
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