Jean-Claude Juncker said such a minister should also be the chairman of all euro zone finance ministers and be accountable to the European Parliament.
The minister would be in charge of economic and financial issues not only for the euro zone, but for all EU countries, Juncker said in a state of the union speech to the European Parliament.
Creating a finance minister for the EU rather than for the euro zone is an attempt to prevent divisions among the 27 countries that will remain in the EU once Britain leaves in 2019, EU officials said.
The idea of a euro zone finance minister has been promoted by French President Emmanuel Macron. He will offer more detailed proposals for reforms to the euro zone on Sept. 26, two days after Germany's federal election, a French diplomatic source said on Wednesday.
Germany Chancellor Angela Merkel also said when she met Macron last month that she could imagine creating a combined European finance and economy minister.
"We need a European minister of economy and finance: a European minister that promotes and supports structural reforms in our member states," Juncker said. "The new minister should coordinate all EU financial instruments that can be deployed when a member state is in a recession or hit by a fundamental crisis."
He said that instead of creating a new post, the job should be given to a vice president of the European Commission -- a suggestion that is bound to meet with vehement resistance from euro zone governments, especially Berlin.
His comments are part of the debate on the future shape of the 19-country euro zone, which Juncker said should expand to take in all the other EU members that are not yet part of it and do not have a formal option to opt out of using the euro.
"Member states that want to join the euro must be able to do so. This is why I am proposing to create a Euro-accession instrument, offering technical and even financial assistance," Juncker said, without giving details.
He said that by the time Britain leaves the EU in March 2019, euro zone membership and participation in the EU's banking union - which entails a single EU supervisor, resolution authority and deposit guarantee scheme - should be the norm for all EU members.
But even though all non-euro zone countries of the EU except Denmark are legally obliged to join the euro when they meet a set of criteria, some of the biggest, like Sweden and Poland, have no plans to do so in the foreseeable future, believing their own currency gives their economies more flexibility.
Addressing French and German ideas of creating a separate budget for the euro zone, on top of the existing long-term EU budget, and a separate euro zone parliament, alongside the existing EU parliament, Juncker rejected both.
"We do not need a budget for the euro area but a strong euro area budget line within the EU budget. I am also not fond of the idea of having a separate euro area parliament. The parliament of the euro area is the European Parliament," he said.
He said the euro zone bailout fund -- the European Stability Mechanism (ESM) -- should be transformed into a European Monetary Fund and become an EU institution, rather than an intergovernmental one as the ESM is now.
The future European finance minister would be in change of the new European Monetary Fund (EMF) as well, he said.
He did not give more details of the new tasks the EMF could take on, saying only the Commission would make a proposal on that, as well as the prerogatives of a European finance minister, in December.
Euro zone finance ministers will open a debate on the future of the single currency area on Friday at an informal meeting in the Estonian capital of Tallinn.
(Writing by Jan Strupczewski; Editing by Mark Trevelyan)
By Alastair Macdonald