The defensive linchpin also missed the vast majority of last season with a knee complaint, and Shearer thinks that United do not have sufficient cover to make up for his absence.
He told The Sun: "With the loss of Vidic now for two months I am even more convinced that the Premier League trophy will either be staying put or heading to Stamford Bridge.
"Before the season started I did not think they were strong enough to win the title despite all their new signings.
"It is early days in the title race but already Manchester United have been dealt a huge blow from which they will not recover."
United face a difficult trip to Shearer's former club Newcastle United in their next Premier League encounter on Sunday, October 7.