The 25-year-old man reportedly calls himself Harald Hitler.
The man, sporting a side parting and a trademark moustache, had been seen having his photograph taken outside the house in Braunau am Inn in which Adolf Hitler was born.
The lookalike had recently moved to the town on the German border, police spokesman David Furtner told the BBC.
Mr Furtner said this was not a joke or a piece of performance art.
"The young man knows exactly what he is doing," the police spokesman said.
He said the man had also been spotted in Vienna and Graz.
Pictures of the man were published by Austria's Heute.at news website on Monday.
Glorifying the Nazi era is a crime in Austria.
Last October, the Austrian authorities decided to demolish Hitler's birthplace house to stop it becoming a focal point for neo-Nazis.
Hitler was born in a rented room on the top floor of the building on 20 April 1889.
During Nazi rule, the house was transformed into a shrine to Hitler as the town drew in a wave of tourists.
But as the Nazis began to lose control in 1944, it was shut.