According to Variety, the film will focus on founder Hilly Kristal, whose club became a huge fixture in the punk and rock scene, hosting such bands as The Ramones, The Sex Pistols and Blondie.
Rupert Grint has also signed on to star as guitarist Cheetah Chrome of the punk band Dead Boys.
Joel David Moore and Julian Acosta will play Joey and Johnny Ramone, while Seinfeld actress Estelle Harris will take on the role of Hilly's mother Bertha.
Production on CBGB will begin next month in Savannah, Georgia.
Akerman, 34, is best known for roles in The Watchmen and 27 Dresses.
She was attached to the lead role in Linda Lovelace biopic Inferno, but has said that the project may be stalled due to the upcoming movie Lovelace starring Amanda Seyfried.
Akerman will next be seen in Rock of Ages alongside Tom Cruise, Alec Baldwin and Catherine Zeta-Jones.
Watch a trailer for Rock of Ages below: