The 34-year-old believes that it is time for the centre-back to to become the team's new leader.
"It's a personal decision from myself," Monk told the club's official website. "The way I look at being a captain, you should consistently be on the pitch. Ash has been consistent on the pitch over a number of years.
"I've said a few times I've not played as much as I would have liked, but I've still contributed in a number of games. But, overall, I feel the team captain should be someone who is on there as a figure of continuity. Ash is that."
Monk has had the captain's armband for seven years.