Several of the Conservative Party lawmakers hoping to replace May in Number 10 have argued they might yet be able to get better terms from divorce negotiations with the EU.
But Juncker, in an interview with Politico, insisted the deal that May signed in November but failed to get past the UK parliament is the only one on the table.
"We have concluded the Withdrawal Agreement with Theresa May," the head of the EU executive said.
"This is not a treaty between Theresa May and Juncker, this is a treaty between the UK and the EU. It has to be respected by whoever will be the next British prime minister.
"There will be no renegotiation as far as the content of the Withdrawal Agreement is concerned."
As things stand, Britain will leave the European Union on October 31 when the latest extension to the withdrawal process expires.
If May's government or its successor has not passed a bill ratifying the treaty, then Britain's membership will end without a transition period or follow-on deal.
Economists on both sides of the Channel warn this could have dire economic consequences, with disruption to trade and supply chains.
But former foreign minister Boris Johnson, the frontrunner to replace May, and some of his rivals insist they will not ask for another extension.
Instead they hope to renegotiate the terms of the agreement to remove or water down the so-called "Irish backstop" clause that would keep the Northern Irish land frontier open with EU member Ireland.
EU leaders have repeatedly said they will not reopen the withdrawal agreement, although they may agree to flesh out an accompanying non-binding road-map towards future ties.