The couple were the subject of break-up rumours last week due to two articles published by The New York Daily News, where a source claimed to have had an affair with Hounsou.
Hounsou has hit back at those reports in a statement to Global Global, in which he labelled any suggestion of infidelity as "vicious lies".
"Any and all claims are totally fabricated and for the press to be spreading these lies is irresponsible on their part," Hounsou insisted. "I am a man of integrity and would never betray my wife or my family."
The Tempest star and Simmons first began dating in 2007 and welcomed a son, Kenzo Lee Hounsou, in May 2009.
Hounsou and Simmons have never married, but they live together.
Life in the Fab Lane star Simmons is the ex-wife of Def Jam co-founder Russell Simmons, whom she divorced in January 2009.