Al-Mohannadi, a vice-president of the Asian Football Confederation (AFC) and Qatar Football Association (QFA), had previously been barred from standing for a place on the FIFA Council while his conduct over the matter was investigated.
Al-Mohannadi has denied wrongdoing.
His disqualification in September led delegates to call off an extraordinary AFC Congress which had been called to choose three Asian places on the FIFA Council. The agenda was voted down after just 27 minutes of the Congress in Goa.
Those places remain unfilled and the elections will now take place at the end of February, one month after the FIFA Council is expected to make key decisions on the size and format of the World Cup.
The new 36-member FIFA Council, charged with setting the overall strategic direction of world football, has replaced the discredited executive committee after a succession of scandals at soccer's governing body.
The ethics committee said in a statement that Al-Mohannadi "did not cooperate with the investigatory chamber in the proceedings against a third party" and had infringed two articles of the FIFA code of ethics.
In addition to the one-year ban, FIFA's ethics judge Hans-Joachim Eckert also fined Al-Mohannadi 20,000 Swiss francs (16,001 pound), although ethics investigators had asked for a two-and-a-half year ban.
The ethics committee has not given further details of the investigation that Al-Mohannadi failed to co-operate with, although it has said that it did not concern the 2022 World Cup, awarded to Qatar.
(Reporting by Michael Shields and Brian Homewood, editing by Pritha Sarkar)
