"A preliminary investigation started yesterday," local prosecutor Patrick Quincy told AFP, as authorities opened a case file on a drunken night out by a group of British men in the French Alpine ski resort of Val Thorens.
The investigation was launched following a complaint from French anti-racism group SOS Racisme. Quincy said he had been unaware of the incident before the complaint.
"I was not at all informed of this incident, which did not cause a fuss in Val Thorens," he said.
Burley, 32, was sacked from his role as a parliamentary private secretary to Transport Secretary Justine Greening, after pictures taken at the party earlier this month were published in the British press.
Burley, a lawmaker in Cameron's centre-right Conservatives, represents Cannock Chase in Staffordshire, central England.
British stag parties, held before a man gets married, are typically jovial, boozy nights out, often with the groom-to-be in embarrassing fancy dress.
Burley was photographed sitting next to the stag, who was wearing the uniform of a World War II-era Germany SS officer -- an apparent offence in France, where Nazi regalia is banned.
The Conservative Party said in a statement that Burley was removed from his post because of his "offensive and foolish" behaviour at the party.
Prime Minister David Cameron also asked for a full investigation.
Burley issued an "unreserved, wholehearted and fulsome apology" over the party, in a letter to the Jewish Chronicle newspaper.
"What was happening was wrong and I should have completely dissociated myself from it. I had a choice, and I made the wrong choice not to leave. I apologize for this error of judgment," he wrote.