Stephen Keshi led Nigeria to this year's African Cup title. (AFP)
Keshi also said the rival should go back to his native Belgium.
Fifa declined to comment further and only said on Wednesday it had received the complaint against Keshi, who led Nigeria to this year's African Cup title.
Malawi coach Tom Saintfiet said the Football Association of Malawi reported Keshi for comments apparently made on an African TV show, where Keshi said Saintfiet was "crazy" and "mad" for suggesting the Nigerian city of Calabar was unsafe for a World Cup qualifier between the countries.
Keshi went on to say the Belgian "is not an African person, he is a white dude. He should go back to Belgium".
In February, Keshi spoke out against the appointment of "mediocre" European coaches by African teams.
"I am never against white coaches in Africa," said Keshi at the time. "I am happy to work with a quality, experienced white coach, who is better than me, so that I can learn from him.
"But what I don't accept is when you bring in a mediocre 'carpentry' coach from Europe, and tell me that he's better than me. I won't accept that. Meanwhile we have quality African former players, who can do the same thing, but you don't give them the opportunity because they're just black dudes. I don't like that."
Keshi, who has previously coached Mali and Togo, qualified Togo for the 2006 World Cup, but was replaced before the finals by German Otto Pfister, who lost all three games. – Sapa-AP