The Scot believes the centre-back's professionalism means he will continue to contribute to the English champions until he leaves at the end of the season
Vidic confirmed on Thursday that he will be moving on when his contract expires at the end of the season, bringing eight years of service at Old Trafford to a close.
But Moyes has no concerns about the defender's commitment and confirmed that he will continue as captain.
"No, [I would not take away the captaincy from] somebody like Vida given the type of man he is," he told the club's official website.
"He’s a great leader for this club and served the club really well and I would expect that to continue right up until the end of the season.
"I think people know that I’ve got things in my mind that I want to do and things I wanted to change in time. I can’t do it all overnight.
"That wasn’t the reason for this. This was a decision that we mutually decided together. He felt it was the right time for him. We’ll get on with it and we’ll move on."
Moyes also says he was was in contact with Vidic about his decision to quit the club: "It was something we mutually agreed together. I think it was the right decision for both the club and the player.
"What I discussed with him will remain private but he has been a brilliant servant and captain for Manchester United. He is captain and will remain captain until the end of the season. He has been a great player for us and we will continue to play him."
The Red Devils welcome Fulham to Old Trafford on Sunday but Moyes has confirmed that Marouane Fellaini has picked up a groin problem which has delayed his comeback from back and wrist injuries.
Jonny Evans will also miss out, but Phil Jones has trained on Friday and will be monitored in the build-up to the game.