The fifth-seeded Clijsters was examined by a trainer at courtside after the second set for an apparent left thigh injury, then took a six-minute medical break. She returned with her upper leg wrapped and completed the third set, but clearly lacked her usual mobility.
"I don't like to give up," Clijsters said. "If something really bad happens, if you twist your ankle. But I was still able to move, still able to hit the ball, so I don't believe in giving up."
The Belgian star, who had dominated the opening set, was coming off a victory last week in Cincinnati. Combined with a win at Miami earlier this year, she had won 13 consecutive matches played on hardcourts.
She said the injury wouldn't keep her from defending her U.S. Open title. She hopes to be back hitting balls in practice by Wednesday.
"It's the hip," she said. "I was trying to get an MRI this weekend but the hospitals here are full, so I'm going to get it done at the beginning of the next week in New Jersey."
Zvonareva will play the winner of a match between Victoria Azarenka and Marion Bartoli.
Clijsters has had some bad luck at the Rogers Cup. In 2006, the last time she played the event on the alternate years it is held in Montreal, she fell and injured a wrist. That injury contributed to her decision the following year to take a 25-month break from competition during which she gave birth to her daughter Jada.
She won the 2009 U.S. Open in only her third tournament after her return.
By reaching the quarterfinals this week, Clijsters is projected to move into the No. 3 spot in the WTA rankings. The last time she was ranked that high was on Aug. 28, 2006.
The eighth-seeded Zvonareva had lost five straight times to Clijsters but now has beaten her twice in a row. She also won in the quarterfinals at Wimbledon this year.
Earlier, Svetlana Kuznetsova reached the semifinals for the first time in eight Rogers Cup appearances with a 6-1, 6-3 victory over unseeded Zheng Jie of China. The 11th-seeded Kuznetsova has won all six career meetings with Zheng, all played on hardcourts.
"I know she's getting better and better," Kuznetsova said. "Before you could beat her easily but the last few times it's been harder and harder."
The 25-year-old Russian turned around a weak season with a victory two weeks ago in San Diego — her 13th career tournament win including the 2004 U.S. Open and the 2009 French Open.
"Winning matches makes you a totally different player," said Kuznetsova, who went through a string of first-round losses and coaching changes. "Without matches, you struggle a lot.
"Maybe you know what to do but you're not confident with some shots. There's only two or three points difference but it makes a huge difference."