Mulumbu, who was born in Zaire, represented France at Under-21 level before opting to play for Congo.
He won the first of his 12 caps in 2008, but has decided not to continue on the international stage in order to focus on his club career and for family reasons.
"This decision has been taken following long discussions with my family and medical advisers," Mulumbu said.
"I hope to have the opportunity to extend my professional career which is the guarantee for my family's security, by retiring from international commitments.
"It was an extremely hard decision for me to take, but I wish DR Congo and the whole team great success."