Al-Mohannadi, a vice-president of the Asian Football Confederation (AFC) and Qatar Football Association (QFA), was banned by FIFA's ethics watchdog in November for failing to cooperate as a witness in an investigation.
He had previously been disqualified from standing for a place on the FIFA Council while the matter was investigated.
However, FIFA's Appeal Committee said in a statement on Thursday that there was insufficient evidence to establish that Al-Mohannadi had violated the code of ethics. It also lifted a 20,000 Swiss franc (15,950 pound) fine levied against him.
His disqualification in September led delegates to cancel an extraordinary AFC Congress which had been called to choose Asian places on the FIFA Council. The agenda was voted down after just 27 minutes of the Congress in Goa.
The election for four places on the Council will now go ahead in May although the AFC has already published the names of the eight candidates.
The AFC could not immediately be reached to comment on whether Al-Mohannadi would be allowed to stand.
Neither FIFA nor its ethics committee have given further details of the investigation that Al-Mohannadi failed to cooperate with, although it has said that it did not concern the 2022 World Cup awarded to Qatar.
(Reporting by Michael Shields; writing by Brian Homewood; editing by Mark Heinrich)
