Bates, who is celebrating his 24th birthday on Friday, skippered the side during Gary O'Neil's latest injury lay-off, but has now replaced the former Portsmouth midfielder as the club's figurehead.
Mowbray told Boro's official website: "Having spoken to Matthew, he's someone I would like to give the responsibility to.
"He's had a lot of injuries, but he's from the area and he understands and supports the football club.
"I would like to think he's maturing into a footballer who can handle that burden, although having done it myself, I don't really consider captaining the club a burden.
"He's now captain of the team and the club and hopefully that can be a good experience for him."
Source: PA
Source: PA