The video of the men's drunken tirade on a 2010 summer night in Stockholm was published, bit by bit, by the Expressen newspaper this week, triggering a crisis within the Sweden Democrat Party.
The police launched the inquiry on its own initiative after having seen the film clips.
"When crimes come to our attention our task is to try and investigate them as much as possible," Stockholm police spokesman Lars Byström told Sveriges Television (SVT).
The video clips show leading party members Erik Almqvist, Kent Ekeroth and Christian Westling harassing a drunk man, calling a young woman a "whore" and hurling racist abuse at Soran Ismail, a stand-up comedian.
Kent Ekeroth is also seen pushing a woman into the side of a car and, at one point, all three men wield aluminium pipes which they pick up from a construction site on the street.
Almqvist and Westling have stepped down from their political posts, while Ekeroth has taken a "timeout" from politics. The party's youth wing has spoken out against the top leadership.
In an open letter to the members, Sweden Democrat party secretary Björn Söder wrote that the past few days may be the Sweden Democrats' "biggest challenge ever as a political party."
He asked members to stand united and wrote that it is "unfortunate" that the youth wing has openly criticized the party's crisis management.
"What we need now is not a split but to support each other and to show unity in this incredibly difficult period," wrote Söder.
Overall support for the Sweden Democrats and party leader Jimmie Åkesson has weakened in the wake of the scandal.
In a poll by the Novus Group, 40 per cent of 1,000 respondents said that their faith in the party has weakened, while 33 per cent said that their faith in Åkesson has weakened, too.
However, among Sweden Democrat voters, 64 per cent still support Åkesson and 24 per cent said they now have more faith in the Sweden Democrats and its leader.
The Sweden Democrats have demanded to see an uncut and unedited version of the film leaked by Expressen, but the newspaper's editor-in-chief, Thomas Mattsson, called this an "unrealistic demand". He said his paper will not comply.
Mattson told the Resume magazine that the party's demand "presumably reveals that the Sweden Democrats think it is more problematic that Expressen, day after day, reveals more new scandals than there are members of parliament - like Ekeroth and Almqvist - that are stilling being backed by the party?"
While a preliminary police investigation into the three politicians' conduct has been launched, no one is at this point officially suspected of any crime.