Team manager, David Calthorpe, said the 27-year-old has damage to the surface lining of his knee cartilage.
“He will see knee specialist Julian Feller tomorrow to have surgery to repair the damage,” Calthorpe said.
“He will be sideline for up to five weeks which is obviously a big blow for the club as he is such an important player and has been in good form.
“It is an old injury that has flared up over time this season and, unfortunately, it has reached the stage where we need to rectify it.”
Calthorpe said the club plans to aggressively rehabilitate McVeigh to get him back into the side ASAP.
McVeigh has played 174 games after being drafted with pick 9 in 1998.