Deputy chief of staff Samuel Abu Jinapor told reporters that Nyantakyi had been captured on video using the name of the president and other senior government officials to induce "potential investors" to part with money.
Nyantakyi was not immediately available for comment when contacted by Reuters.
The video was recorded by investigative journalist Anas Aremeyaw Anas and is due to be broadcast on June 6.
Its producers told Reuters it was an expose on corruption among Ghana's football officials and their affiliates.
"The president after consultations is fully satisfied that a prima facie basis has been established for criminal investigations to be launched into the conduct of the president of the football association," Jinapor said.
Anas reported on alleged corrupt practices among the Ghanaian judiciary in 2015 that led to the suspension and in some cases dismissal of some judges.
Nyantakyi, who is also a member of the FIFA Organising Committee for Olympic Football and an executive committee member at the Confederation of African Football, has denied similar allegations of corruption in the past.
(Reporting by Kwasi Kpodo; Editing by Toby Davis)
