"We cannot tolerate cherry-picking," the Brussels financial services chief told German business daily Handelsblatt.
"It's up to the British government. If it decides not only to leave the EU but the single market as well, there will be serious effects on the City of London," he said.
London's financial district has benefited from Britain's EU membership as a foothold in the single market for British and non-EU banks.
Huge volumes of euro-denominated trade pass through Britain thanks to so-called "passporting" rules, which allow the UK to host transactions in the single currency despite not itself being a part of the eurozone.
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Without a deal to remain a part of the internal market -- which Dombrovskis insisted must include the "four freedoms" of movement of capital, goods, services and labour -- the City of London risks losing those rights.
Several major players in the sector, including US giant JP Morgan and Swiss UBS, have warned that thousands of jobs could leave the "Square Mile" financial district for the continent if that happens.
Eurozone banking centres including Frankfurt, Paris, Amsterdam and Dublin are all elbowing for position to benefit from any mass exodus from the City.
In the meantime, he said, the UK remains an EU member and will have to implement any and all financial regulation decided on by Brussels.
Britain is also certain to lose the European Banking Authority regulator, Dombrovskis continued, telling Handelsblatt that "all EU authorities must of course be headquartered in the EU".
Dombrovskis' intervention comes on the same day as EU president Donald Tusk travelled to London for talks with May to discuss the Brexit process.