Nyantakyi, a member of FIFA's decision-making Council, also apologised to Ghana president Nana Akufo-Addo and the government for what he called his "indiscretion".
"After a meeting of the Executive Committee this afternoon I decided to resign as President of the Ghana Football Association (GFA),” he said in a statement.
Nyantakyi, who has been GFA president since 2005 and was elected to the FIFA Council in September 2016, was filmed by an investigative journalist in a hotel room appearing to take a $65,000 (£48,544) bribe from a supposed businessman seeking to sponsor the Ghanaian football league.
FIFA said on Friday it was suspending Nyantakyi for 90 days. The Ghanaian government has begun a process to dissolve the national football body, Information Minister Mustapha Abdul-Hamid said on Thursday.
On Friday, Ghana's police locked down the GFA offices, declaring the building a crime scene.
Segments of the recording by undercover journalist Anas Aremeyaw Anas appeared to show Nyantakyi also demanding kickbacks to pass on to top government officials, including the presidency.
Ghana president Nana Akufo-Addo has called for criminal investigations against Nyantakyi.
FIFA has not yet commented on whether any action will be taken over the government's plan to dissolve the GFA.
The global football body does not accept any third party, including government, interference in its member associations.
It could respond by suspending Ghana's membership, which would mean the country's national teams could no longer compete in international competition.
Ghana, who have played at three previous World Cups, missed out on the this year's tournament which starts in Russia on June 14.
(Reporting by Brian Homewood and Kwasi Kpodo,; Editing by Christian Radnedge and Toby Davis)
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