Williams lost 6-4, 6-3 to Svitolina, who is ranked 20th in the world.
Williams was looking to become the first female tennis player to win two gold medals in singles at the Olympics. She won gold in both singles and doubles at the 2012 Olympics in Beijing.
Serena is now out of the Olympics altogether, after also losing in the first round in doubles alongside her sister Venus Williams.
The sisters won gold in doubles in 2000, 2008 and 2012, and had never before lost a doubles match in Olympic play, but went down 6-3, 6-4 on Sunday to Lucie Safarova and Barbora Strycova of the Czech Republic.
Venus also lost in the first round in singles, meaning both Williams sisters are done in Rio. Venus fell to 62nd-ranked Kirsten Flipkens of Belgium after coming down with an illness before the games began.
The sisters entered the 2016 Summer Games tied for most career gold medals among women’s tennis players with four. Neither was able to add to that total at what could be their final Olympics.