"The practice of sport is a human right. Every individual must have the possibility of practicing sport, without discrimination of any kind and in the Olympic spirit, which requires mutual understanding with a spirit of friendship, solidarity and fair play," the quote reads.
Russia's anti-gay policies have been a problem ahead of the Winter Olympics since a gay propaganda law was instituted.
The measure prohibits statements and actions that condone non-traditional lifestyles to minors.
Russian President Vladimir Putin has supported the law, and said gay people are welcome as long as they leave children alone.
The International Olympic Committee has asked athletes not to inject political stances into the games, which has angered gay rights advocates, the Wall Street Journal reported.
Some companies, such as Chobani Yogurt and AT&T, have issued statements condemning the law, but sponsors of the Olympic Committee have not.
Google is not an Olympics sponsor and didn't issue a statement concerning the doodle, the Journal reported.
"It speaks for itself," Svetlana Anurova, a spokeswoman for Google in Russia, said.