Salt Bae, the Turkish chef whose real name is Nusret Gokce, was pictured holding and kissing the World Cup trophy while celebrating with Argentina players after their win over France.
FIFA rules state the trophy can only be held by a very select group of people, including tournament winners, Fifa officials and heads of state.
In a statement to BBC Sport, a Fifa spokesperson said the appropriate internal action will be taken.
Salt Bae owns a chain of luxury steakhouses and rose to fame in 2017 after his technique for preparing and seasoning meat became an internet meme.
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