"The Criminal Investigation Department (CID) of the Ghana Police Service is investigating Mr Kwesi Nyantakyi, President of the Ghana Football Association, for alleged offences, including corruption," said spokesman Sheilla Kessie Abayie-Buckman.
"This follows a complaint received from His Excellency the President of the Republic of Ghana, Nana Addo Dankwa Akufo-Addo, that Mr Nyantakyi has used the President's name and office fraudulently."
No further details were given about the allegations, which follow an investigation by an undercover journalist, Anas Areneyaw Anas, who has previously exposed graft.
There was no immediate comment from the Ghana FA.
Abayie-Buckman said Nyantakyi, who is also a senior member of the Confederation of African Football governing body, was expected to return to Ghana on Wednesday to face questioning.
Akufo-Addo, who came to power in December 2016, has embarked on an anti-corruption drive and in February formally appointed a special prosecutor to look into claims of graft.
An expose by Anas in 2015 into claims of bribery in the judiciary led to the sacking or suspension of dozens of judges.
The case sent shockwaves through the West African nation, which sees itself as a bastion of democracy and good governance in a turbulent region.
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