Researcher Birgit Schwartz has established that "Cupid Complaining to Venus", painted by Lucas Cranach the Elder in around 1525, was once part of Hitler's collection after spotting the work in a photograph of his private gallery.
Now the National Gallery wants to know how it ended up there, amid concerns that the painting may have been one of thousands forcibly seized from Jewish families by the Nazis before and during World War Two.
"There is no direct evidence that it was looted to Hitler's collection, but of course that remains a possibility, and hopefully that information will come to light," said a National Gallery spokesman.
The gallery said on Thursday that it bought the painting in 1963 from New York dealers E & A Silbermann, who said at the time that it was sold to them by descendants of the person who bought the work at auction in 1909.
But recently the gallery learned the painting was actually acquired in 1945 by Patricia Hartwell, then a U.S. war correspondent in Nazi Germany. Hartwell died in 1998.
A relative of Hartwell informed the gallery that in 1945 she was allowed to take the painting from a warehouse full of art then controlled by U.S. forces in southern Germany.
"The provenance gap that now exists is therefore between 1909 and 1945," the gallery said in a statement.
"The National Gallery now wishes to establish how and when Cranach's 'Cupid Complaining to Venus' came to be in Hitler's collection. Any information from the public would be gratefully received.
"In light of concerns that some works of art may have been improperly acquired during 1933-45, the National Gallery, along with museums elsewhere, has paid particular attention to the whereabouts of its paintings during those years."
Some priceless paintings seized by Nazis from Jewish families in Germany and Austria between 1933 and 1945 have been returned to the original owners in recent years.
Some have been sold on the market, including one painting by Austrian artist Gustav Klimt bought privately in 2006 for a record $135 million.
(Reporting by Mike Collett-White, editing by Paul Casciato)