Kassian received a major penalty for boarding and a game misconduct for the hit in the first period of Thursday's game in Dallas.
Dillon was attempting to dump the puck into the Canucks zone before going to the Stars bench when Kassian approached him from behind and drove him hard into the boards.
The NHL says a suspension was warranted because Kassian didn't make any effort to avoid or minimize the contact and hit Dillon with "significant force."
"Kassian has enough time to avoid this check entirely or at the very least minimize his force," the league says in a video on its website.
Dillon was shaken up but did return to the game in the second period.
Kassian has been suspended before for high-sticking and is considered a repeat offender.