American fifth seed Williams, the singles champion in 2000 and, at 36, the oldest woman in the draw, lost to Belgium’s Kirsten Flipkens 4-6, 6-3, 7-6 (7/5) in a three-hour centre court marathon.
Williams, who has also captured three doubles golds with sister Serena, had her opportunities, leading 3-1 in the second set and 4-1 in the decider.
But despite the encouragement of watching US Secretary of State John Kerry, she ran out of steam at the crucial moments, noisily coughing throughout the closing exchanges.
“She had been ill for a few days with a bad virus. She had an upset stomach and she was coughing up a lot, you could see she was really struggling,” said US captain Mary Jo Fernandez, who faced the media in Williams’ place.
Williams now faces a battle to be fit for Sunday’s opening doubles with Serena.
“Fingers crossed, she’ll be OK. I would be highly surprised if she didn’t play. It’s been her goal to play in her fifth Olympics and she wants to win a medal so badly.”
Flipkens was just two points away from defeat in the ninth game of the decider and rated her win as “in the top two” of her career after her victory over Petra Kvitova at Wimbledon in 2013.
“To beat Venus, one of the biggest champions, gives me goosebumps,” said the 30-year-old, playing in her first Olympics.
Fourth seeded Radwanska was also a high-profile casualty, slumping to a 6-4, 7-5 loss against China’s world number 63 Zheng Saisai.
The Pole only arrived in Rio on Wednesday night after having to fly from Montreal, where she competed last week, to New York to Lisbon and then to Rio.
In all, she was on the move for 55 hours and covered around 14,000 kilometres.
“I spent three days in an airport so that was not the best preparation. I could have used more practice,” said former Wimbledon runner-up Radwanska.
– China double –
Zheng’s win was the second top victory of the day for China after national number one Zhang Shuai saved three match points to beat Swiss 12th seed Timea Bacsinszky, 6-7 (4/7), 6-4, 7-6 (9/7).
Italian sixth seed Roberta Vinci, the 2015 US Open runner-up, also exited, going down 7-5, 6-4 to Slovakia’s Anna Karolina Schmiedlova.
There was little equivalent drama in the men’s singles.
Japanese fourth seed Kei Nishikori, a quarter-finalist in London in 2012, breezed past Spanish left-hander Albert Ramos-Vinolas, 6-2, 6-4.
Nishikori next plays Australia’s John Millman, who became the first player to clinch a ‘double bagel’ — 6-0, 6-0 — in Games history.
The 27-year-old Millman swept past Ricardas Berankis in just 50 minutes, making it a miserable summer for the Lithuanian.
At Wimbledon, Berankis was knocked out in the first round by Britain’s world number 772 Marcus Willis, a club professional.
Men’s fifth seed Jo-Wilfried Tsonga overcame a scare from Tunisia’s Malek Jaziri to triumph 4-6, 7-5, 6-3.
Meanwhile, 43-year-old Leander Paes’s seventh Olympics ended quickly when he and Indian partner Rohan Bopanna lost 6-4, 7-6 (8/6) to Lukas Kubot and Marcin Matkowski of Poland.
But another veteran, 35-year-old Martina Hingis, playing in her first Olympics in 20 years, made it through to the second round of the women’s doubles.
She and Bacsinszky defeated Australia’s Samantha Stosur and Daria Gavrilova 6-4, 4-6, 6-2.
Defending champions Andy Murray and Serena Williams, as well as top seed Novak Djokovic and 2008 champion Rafael Nadal all start their campaigns on Sunday.