The suspension is for "a late, illegal check to the head" of Montreal Canadiens defenseman Alexei Emelin during Thursday's game.
Burrows will lose $72,600 while suspended, which instead goes to the Players' Emergency Assistance Fund.
• Off The Draw: Weekend games to watch, more notes
Video of Burrows' check on Emelin is below. No penalty was called on the play, which occurred right before Canucks forward Nick Bonino scored on a passing play.
Burrows will be eligible to return for Vancouver's Nov. 6 game against the San Jose Sharks.
The Canucks (7-3-0) play the Edmonton Oilers (4-5-1) on Saturday.
- Molly Geary