In an episode broadcast on March 18, Mr. Schwarzenegger played host to five of the show's contestants in his private conference room at the Capitol.
The governor denies any link between the donation and the television appearance, but some political watchdog groups are skeptical.
"He's clearly using his personal friendships and his celebrity to pay off his campaign debt, and that's just wrong," said Jamie Court, president of the Foundation for Taxpayer and Consumer Rights, a group that tracks campaign donations.
A Schwarzenegger spokeswoman, Julie Soderlund, said the April 20 donation was not connected to the governor's appearance on the The Apprentice. The taping took place earlier in the year, but Ms. Soderlund was unsure of the date.
The Donald could not be reached for comment at his company's headquarters in New York.
The donation was Mr. Trump's first to Mr. Schwarzenegger, whom he described as a great friend when he told a group of contestants that they would meet him as a reward for winning a competition.