The tweet, sent at 12.29pm, said that Islamist extremism was "a real threat to our way of life" and urged voters to "act now before we see an Orlando-style atrocity here before too long", was deleted around an hour after being posted.
Migration and the UK's ability to control its borders is one of the key concerns of leave campaigners.
The tweet was then deleted, following criticism from counterpart Britain Stronger In Europe.
Education secretary Nicky Morgan said: "Using the tragic deaths of innocent people to make a political point is simply shameful. Leave.EU must apologise for the hurt they have caused and apologise immediately."
She also said that official Brexit group Vote Leave should "condemn such despicable tactics and make clear that the Orlando attack has nothing whatsoever to do with the EU debate in this country".
And Labour MP Chris Bryant said: "Leave.EU’s tweet is completely out of order. Do they have no sense of common decency? They should take it down and apologise immediately.
"The wider Leave campaign should condemn it in the strongest possible terms. If they do not, they will be endorsing the twisting of the murders of innocent people for political purposes."
The Leave.EU press team was not immediately available for comment. A spokesman for Vote Leave, the official Brexit campaign, declined to comment when contacted by PRWeek shortly after the tweet was published.