Sulaiman's son, Mauricio Sulaiman, said the man, who many say raised the profile of the sport in his four-decade leadership at the Mexico-based council, died at a hospital in Los Angeles.
He had been hospitalised at the University of California, Los Angeles Medical Center for months for a heart condition.
The WBC confirmed his death, calling him the ''father of boxing''. Sulaiman was a member of boxing's Hall of Fame since 2006.
''He certainly treated all fighters as his sons and daughters, he suffered from their problems and worked every single day of his life to try to make boxing better and safer,'' the council said in a statement.
The son of a Syrian mother and a Lebanese father, Sulaiman was born on May 30 in Ciudad Victoria, Mexico.
He boxed as an amateur but quickly shifted over to working as a manager and a referee.
He trained and promoted many fighters.
Sulaiman is known for supporting Julio Cesar Chavez, Mexico's most famous boxer, and then the fighter's son, Julio Cesar Chavez Jr
Chavez was among the first fighters to tweet a message, sending his condolences and calling him his ''second family''.
''Rest in peace, my dear 'licenciado' Balin, like I used to call him with a lot of love,'' read a message posted on Chavez's account.
Most recently, Sulaiman helped Saul 'Canelo' Alvarez, a young champion who last year challenged Floyd Mayweather Jr in one of the richest fights ever. He lost to Mayweather.
Sulaiman also managed to institute new rules and regulations regarding boxers' safety and welfare. Among these changes was the reduction in the number of rounds from 15 to 12.
In Bangkok, WBC vice president Pol Gen Kovid Bhakdibhumi said the passing of Sulaiman, who visited Thailand on several occasions, completed the cycle of a great leader of boxing that is unlikely to surpass for achievements.
''Dr Sulaiman supported and instigated the rise of Thailand boxers into the ranks of world boxing, and many great Thai world champions over the past four decades owe their success to Dr Sulaiman who considered Thailand to be his second home,'' he said in a statement.
''Thailand boxing mourns the passing of a great leader. Dr Sulaiman will be remembered for his unstinting generosity to the poor. He was the shinning star and great hope for hundreds of Thai boxers who dreamt of becoming a WBC world champion.''
Kovid said the decision of the WBC under Sulaiman's leadership to create a Muay Thai division had put the Thai national martial art on the world stage.