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.
Millions of Getty images now available for free via embed tool
Ray Liotta sues skin care company over use of likeness