The sanction was handed down after Bourque had a hearing league's Department of Player Safety. It's the second time in less than a month the 30-year-old winger has been suspended.
The latest discipline was for delivering an elbow to the head of Washington forward Nicklas Backstrom in Tuesday's 3-1 Capitals' victory.
Bourque was suspended for two games after a Dec. 18 incident in which he checked Chicago defenseman Brent Seabrook from behind.
The Calgary player won't eligible to return to action until the Flames' Jan. 17 contest against San Jose.