The 34-year-old has been skipper since 2006 and will remain the club captain going into his 10th season with the Swans but the Wales international will now lead the team out even when both are playing.
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"I just feel it's the right time now. It is a difficult decision," he told BBC Sport.
"It's probably been one of my proudest things I've had to do with Swansea City. I know we've had promotions and cups but it's definitely up there to have captained this club for so long. It's been a real honour.
"If the manager thinks I'm wrong then I'll have to listen, won't I? But that's my gut feeling, anyway. My duties as club captain won't change. I'll still be doing the stuff off the pitch with the boys and in the community representing the club."
"I just feel from my experience as team captain that the continuity should be there with someone that's been there week in, week out, which has been Ashley. Obviously, when I've not played, he wears the captain's armband - I just feel that should continue even when I am playing. "
Monk made only 15 appearances last season for the Swans, who have added another centre-back in Jordi Amat from Espanyol, but the experienced defender signed extended his contract until the summer of 2015 in February and insists that he still has a contribution to make.
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"That's all I can ask of myself, make sure that I'm fit, ready, look after myself and when called upon to do it right. I've done that so far, so I can't have any complaints with myself.
"If I couldn't compete at this level, if I was slacking off and feeling physically not right then I'd hold my hand up, I'm honest enough to do that. But I think I've proved the last couple of seasons in the Premiership that, when I've played, I've more than competed with some of the top strikers.
"I probably feel even stronger this pre-season. I feel sharp, I've looked after myself through the summer and I feel fit."