The Serbian is leaving Old Trafford at the end of the season and Rooney has been backed to take the armband now that he has committed his future to United.
The 28-year-old striker has signed a new five-and-a-half-year contract with the Red Devils, a deal which Vidic feels is important for club and player, and the defender says that Rooney is a natural leader.
"Wayne is a big player and it is important for him to stay," Vidic told Sky Sports News. "Wayne has signed a long-term contract and he will be one of the most important players in the next few years."
Questioned on the possibility of Rooney replacing him as captain, Vidic added: "Obviously it is the manager's decision and he has to choose his captain.
"Wayne is one of the leaders in the team and I will not be surprised if he becomes captain."
Rooney's new contract with the Premier League champions is worth a reported £300,000 per week.