Muntari was booked for complaining about racist abuse during a match at Cagliari and subsequently suspended, although that sanction was later lifted.
The Ghanaian then walked off the field in protest in the final minutes of the game.
Infantino told reporters on Tuesday that he intended to talk with Muntari and would give him FIFA's "full solidarity".
The FIFA president also said he would be discussing the issue with Italian Football Federation President Carlo Tavecchio about the issue.
"Of course I will speak to Tavecchio, I will speak to Muntari as well... we will work together," Infantino, who is in Bahrain for Thursday's FIFA Congress, said.
Asked what could be done about the issue, Infantino said: "Fight. Continue to fight. It's good to bring these things out when they happen. We have to work. We have to work on the people."
Infantino said the protocol, established by UEFA in Europe, with a series of stadium announcements leading up to a possible stopping of the game, should be applied.
"Unfortunately idiots, there are always idiots everywhere but we have to fight them," he said.
Muntari said he had complained that parts of the crowd, including a group of children, had hurled racist insults at him from the start of the game in Cagliari on April 30.
The player said the referee told him to stop talking to the crowd and ended up showing him the yellow card for dissent in the 90th minute.
The decision to punish Muntari has been widely criticised and the player himself has said FIFA and UEFA are not taking the issue of racism seriously.
But FIFA Secretary General Fatma Samoura rejected that charge and said the organisation had the structures to deal with the problem.
"I don't have to call people anytime that they have been victim of an abuse. We have a committee that is in charge of monitoring those actions. And the committee will take action," she told reporters.
"We've been very severe in Europe, in Latin America - we've been regularly publicising the action of the committee on every action that relates to racism, homophobic chants and any kind of discrimination," she added.
Asked for her personal view on the Muntari case, the Senegalese official said that was irrelevant.
"My personal view does not matter. What matters is that the disciplinary committee has to act and the sooner the better," she said.
"I have my personal feelings on anybody that is treated like he has been treated, on the pitch and off the pitch but I'm not here for my personal matters.
"I'm here to make sure that FIFA takes through the committee the appropriate action for any single discriminatory action."
(Editing by Sudipto Ganguly)
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