Mr Schapiro will leave at the end of August to "pursue a new challenge outside the shipping business," the report said, quoting a company spokesman.
It is not known whether Mr Schapiro's departure is linked to tumultuous talks with potential investors to reschedule the financially troubled carrier's formidable debt of US$5.3 billion, accrued from one of the largest order books in the industry.
CMA CGM has until the end of July to meet a deadline for outside investment or face more stringent measures from lenders.
The shipping line, the third largest in the world after Maersk and MSC, said it would announce when a replacement CFO when one it found one.
Tradewinds also reported it is nearing a deal for the French sovereign wealth fund FSI and another unnamed partner to become investors, while other news outlets said founder and chairman Jacques Saade had broken off talks with a Qatar fund for similar investment.