Japanese plastic surgeon Katsuya Takasu wants to reward the team after hearing about their financial difficulties.
He will pay them $20,000 (£15,350) for silver and $10,000 (£7,680) for bronze.
Takasu told BBC Sport the $200,000 "is a special donation" and "it is better to deliver it to the team personally".
He added: I've made previous donations to a Japanese hockey team and other notable causes in the past but this right now with Nigeria is incredibly passionate for me.
"I am deeply determined to motivate this indomitable and strong Nigerian team. I don't want to distract them but to push them further to their target - the gold in Brazil.