He is expected to be succeeded by Jean Lemierre, a senior adviser to Prot.
A spokeswoman for BNP Paribas did not respond to a request for a statement.
In July, BNP Paribas was hit with a record $8.97bn (£5.2bn, €6.5bn) fine for violating US sanctions between 2004 and 2012.
The French bank repeatedly broke longstanding sanctions against Sudan, Cuba, and Iran and engaged in a “complex and pervasive scheme to illegally move billions through the US financial system”, the attorney general at the US Justice Department, Eric Holder said in a press statement at the time.
Prot joined BNP Paribas in 1983 and later become chief executive officer from 2003 to 2011.