The 26-year-old is arguably the best player in the world at the moment, already scoring 17 goals and providing two assists in his 16 games so far this season.
Mbappe 31 league goals in his first season at the club saw him recently beat Mohamed Salah and Robert Lewandowski to claim the 2024-25 European Golden Boot award.
Speaking at the ceremony, the Frenchman said he is targeting "collective prizes" at Real Madrid and stated his ambition to remain at the club for years to come.
"It's an important moment for me; the first time I win this prize. It means a lot to me as a forward," said Mbappe.
"We have an incredible group. I hope we're going to win important prizes this year. That's the most important thing, winning collective prizes.
"I hope to be here for many years and win this kind of thing many times. I hope we'll keep going as a team. As I say, the team is the most important thing.
"Without these players, it's impossible to win these prizes. I know that. I want to thank the club, the doctors, the staff who help me on and off the pitch. I hope I'll win it again, next year, I've started well!"