A condition of the deal is that if the Blue Jackets are able to sign the potential unrestricted free agent to a contract, the pick will be in the fifth round next year rather than the seventh.
The Canadiens obtained Wisniewski from the New York Islanders on Dec. 28 for a second-round pick and a conditional fifth-round selection. The power-play specialist had 51 points (10 goals, 41 assists) in 75 games last season.
He earned $3.25 million last season.
The Canadiens were not expected to try to retain Wisniewski after they made a contract offer this week to veteran Roman Hamrlik, who can also become an unrestricted free agent on Friday.