The disciplinary action stems from a category one penalty for physical abuse of an official during a playoff game against the Barrie Colts on April 10.
Baird, who was suspended indefinitely after the incident, is ineligible to play in the post-season. The ban includes the six games that the Battalion have played since April 11.
North Bay is scheduled to open the best-of-seven OHL final on Thursday at Guelph.
The series winner will advance to the MasterCard Memorial Cup next month.
Baird, a six-foot-two 178-pound native of Cayuga, Ont., had one assist and 27 penalty minutes in 28 games with the Battalion this past season.