According to TMZ, this fight went down during the band's Terminal 5 show in NYC last week.
View this video on YouTube
The altercation happens around 8:10 on the video. Ken Casey, the Dropkick Murphys bassist, starts walking across the stage.
Casey then bodyslams the nazi, hands his bass over to a person in the crowd, and chases the nazi out of the crowd.
Everyone notices what's going on and the band stops their cover of AC/DC's "T.N.T."
Security rushes in and then the concert resumes.
The lesson here being: if you're a nazi, don't be a nazi.
(h/t Heyveronica)