Dubinsky and Kassian tussled late in the third period of the Oilers' 7-2 win. It appeared that Kassian's first punch did the damage, with Dubinsky covering up until they could be separated. Each were given five-minute fighting penalties.
Columbus put Dubinsky on injured reserve Wednesday.
The 31-year-old Dubinsky has three goals and nine assists in 31 games this season. He had 41 points last year.
Columbus is second in the Metropolitan Division with 39 points.