Williams, who is ranked 58th in the world, was able to break Vesnina's serve only once. Vesnina, who is ranked 78th, broke Williams' serve five times.
It was Williams' earliest loss since her first Wimbledon appearance 15 years ago.
Williams suffers from the autoimmune disease Sjogren's syndrome, which can cause extreme fatigue and joint pain.
When asked Monday whether she'll continue to play after the Olympics in London next month, Williams, a seven-time Grand Slam champion, remained optimistic.
"I feel like I am a great player," she said. "I am a great player. Unfortunately, I had to deal with circumstances that people don't normally have to deal with in this sport.
"But I can't be discouraged by that, so I'm up for challenges. I have great tennis in me. I just need the opportunity. There's no way I'm just going to sit down and give up just because I have a hard time" in her first tournaments since missing the end of the 2011 season.
"You know, that's just not me," she said.