The 38-year-old, who lifted the One-Day Cup at Lord's last weekend, is retiring at the end of the season.
Notts says the decision will allow the club to look to the future.
"Chris and I have had a chat. We agree that this a great fit for everyone as we prepare for a T20 campaign", said head coach Peter Moores.
Moores' son, 20-year-old Tom, will keep wicket for Notts as they begin their Twenty20 campaign against Yorkshire at Headingley.
"The thinking is that it allows us to plan ahead for the future, with Chris due to retire in September, yet it enables Chris to pass on his vast experience and knowledge to our players," Peter Moores added.
"He's excited about taking on this new role. It's a good opportunity for him to develop his coaching skills and allows Chris to rest and recharge his batteries after a very busy period.
"He'll be fresh and ready to captain the side when the County Championship matches restart in August."
Notts Outlaws wicketkeeper Chris Read will be part of the club's coaching staff rather than play in this season's T20 Blast, which begins on Friday.