The NHL announced the punishment Sunday, Seabrook's 29th birthday.
Seabrook received a five-minute major and game misconduct penalty for a vicious elbow to Backes' head late in the third period of Saturday's Game 2. Backes had to be helped off the ice and did not return during St. Louis' 4-3 overtime victory.
Seabrook's penalty led to Vladimir Tarasenko's tying goal with 6.4 seconds left in regulation.
The suspension is a big blow for the Blackhawks, who are down 2-0 heading into Game 3 on Monday night. Seabrook had a goal and an assist in each of the first two games of the series.