Chwalińska, who received a wild card into the tournament and was seeded No. 20, lost 6-2, 5-7, 2-6 to the world No. 164, who advanced through qualifying.
The turning point came in the second set when Chwalińska led 5-2 and held a match point on Sawangkaew's serve.
During the rally, the Pole slipped while moving to her left and appeared to injure her right ankle.
Although she got back on her feet and continued playing, she lost the game and called for a medical timeout to receive treatment on her ankle.
Sawangkaew won the next five games to take the second set as Chwalińska's movement became increasingly restricted.
The Polish player briefly regained momentum by taking a 2-0 lead in the deciding set, but she was hampered by pain and was unable to win another game, eventually losing after 2 hours and 40 minutes.
Despite her physical problems, Chwalińska chose not to retire from the match.
Polish fans in the stands applauded her off the court, chanting "Thank you, thank you."
Speaking after the match, Chwalińska said the cramps had proved more debilitating than the ankle injury.
"By the end of the second set, I started cramping all over my body," she told reporters. "I don't think it was purely physical. Stress also played a part, along with the intense period before Wimbledon because my preparations weren't perfect. It was one of the toughest matches of my career."
She added that she had never before experienced cramps severe enough to limit her game.
"This is Wimbledon, and I didn't want to retire," Chwalińska said. "I knew I wasn't risking my health by continuing. I would have regretted retiring, so I wanted to keep playing."
The 25-year-old, who reached the French Open final three weeks ago, said the recent surge of attention had made preparations for Wimbledon more challenging, but added she had no regrets about her efforts.
Chwalińska is also entered in the women's doubles competition alongside Austria's Sinja Kraus, but said it was too early to decide whether she would play, with her participation depending on the condition of her injured ankle.
Wimbledon, the only Grand Slam tennis tournament played on grass, opened on Monday and runs until July 12.
(gs)