Braun has been dealing with a strained left calf for a week.
Brewers general manager Doug Melvin said he had a discussion with Braun and trainer Roger Caplinger to reach the decision. Braun was disappointed he had to pull out after being the NL's top vote-getter, but didn't want to risk aggravating the injury.
Melvin says Braun will go to the All-Star festivities, but would've been required to play three innings instead of taking a bench role to stay on the team, precipitating his decision.
Atlanta's Jones had to be replaced after he had surgery Saturday on a torn meniscus in his right knee.
It will be Rolen's seventh All-Star trip in a 16-year career, while the 24-year old McCutchen will be making his first All-Star appearance in three major league seasons.
McCutchen joins right-hander Joel Hanrahan in representing Pittsburgh. Entering play Saturday, McCutchen was batting .292 with 13 home runs and 49 RBIs. He also had 15 stolen bases and has reached based safely in 19 straight games, including Saturday night against the Chicago Cubs.
Rolen, the Reds' fourth All-Star participant, is batting .245 with five home runs and 35 RBIs in 60 games this season.
NL manager Bruce Bochy chose McCutchen because Braun was a fan-elected starter. However, Rolen made the team because he was the next-ranked third baseman on the NL ballot after Jones was placed on the disabled list Saturday.
The All-Star Game is Tuesday night at 8 p.m. ET at Chase Field in Phoenix, home of the Arizona Diamondbacks.
Information from The Associated Press contributed to this report.