The Spurs said a timeline for Parker's return would be determined at a later date. The team said he underwent successful surgery on the tendon Friday.
With 8:52 left in the fourth quarter, Parker immediately clutched at his left knee after a driving floater over Patrick Beverley and collapsed to the court, where he lay motionless for several minutes.
Said coach Gregg Popovich after the game: "It's not good."
Houston will host Game 3 of the best-of-seven series Friday night.
"You never want to see a player injured, especially a guy like TP, who is closing down at the end of his career," Houston star James Harden said. "He's been playing well all postseason. It's tough. We say a prayer for him."
Said Rockets coach Mike D'Antoni: "I hate it for Tony Parker. He's a great guy; not [just] a good guy."
After the Spurs were blown out in Game 1, Parker responded with 18 points in 26 minutes before getting injured to help San Antonio rebound and even the series.
His 10.1 points per game in the regular season was his lowest average since his rookie year in 2001-02. But he averaged 15.9 points on 53 percent shooting in eight playoff games -- second on the Spurs behind Kawhi Leonard (30.3 PPG) -- and had a vintage 27-point night in Game 6 against Memphis to clinch that series.
On Wednesday, Parker became the ninth player in NBA postseason history to reach 4,000 career points. He and LeBron James are now the league's only players to have scored 4,000 points and dished 1,000 assists in postseason play.
Parker had not only played 221 career postseason games, which ranks fifth in NBA history, but he had also never missed a playoff game in his 16 seasons with the Spurs.
He missed 16 games during the regular season because of rest and various ailments, such as right knee soreness, a left quadriceps bruise, a left knee bruise, left foot pain and back stiffness.
Most likely to get the first crack at replacing Parker in the lineup is veteran Patty Mills, who averaged 9.5 points and 3.5 assists per game during the regular season and contributed seven points Wednesday against the Rockets.
Leonard also said he could "definitely" see himself in a point-forward role with Parker out.
If Mills moves to the starting lineup, Manu Ginobili likely will serve as the primary backup.
Rockets players, referring to Popovich and the Spurs as a "machine," said they didn't think much would change with Parker out.
"You know how Pop is," Beverley said. "His team is a machine. One person falls down, next person steps up."
Said Harden: "You can take anybody off that roster, and they're [still] a great team."
One Houston player who disagreed, however, was forward Trevor Ariza, who said Parker's loss leaves a "huge hole" for the Spurs.
"What he brings to their team, I don't know how you replace that," Ariza said. "Not saying they don't have good enough players to step in. But what he brought to that team, I think it's unmatched."
Parker's injury puts the Spurs in a difficult spot this offseason because they have no cap room to go after a guard, especially with Pau Gasol expected to opt in for $14 million. If the injury is deemed to be career-ending, the Spurs can't even apply for salary-cap relief until one year from the date of the injury.
ESPN's Michael C. Wright and The Associated Press contributed to this report.