The forward, who joined the West London side from Marseille earlier this week, said that he faced Fernandes on the football game at his home in the south of France.
"I don't know if I should say who won, because he might get angry," said Remy, 26.
"We played two matches and I won them both. That wasn't something I expected - to have the chairman come to my house will stay with me as one of the great memories from my football career. It's true he is ambitious, but he's also very humble.
"He's quite good [at FIFA] - he could certainly be a match for some of my friends."