Mrs May said the vote would have “grave” implications and the “legal default” was that the UK would leave on 12 April.
That meant there would not be enough time to get legislation through to avoid a no-deal Brexit, she said.
Labour leader Jeremy Corbyn called for her to resign and call an election.
Responding to the vote, European Council President Donald Tusk tweeted: “In view of the rejection of the Withdrawal Agreement by the House of Commons, I have decided to call a European Council on 10 April.”
The result of the vote means the UK has missed an EU deadline to secure an extension of the Brexit process and leave with a deal on 22 May.
Mrs May now has until 12 April to seek a longer extension to the negotiation process to avoid a no-deal Brexit on that date.
With a clear majority in the Commons against a no-deal Brexit, and with MPs holding more votes on alternative plans on Monday, Mrs May said that the UK would have to find “an alternative way forward”.
This was “almost certain” to involve to hold European Parliament elections in May, she said.
The prime minister said that the outcome was “a matter of profound regret”.