Parker will have a scan on Wednesday after tweaking his right hamstring during the victory that gave San Antonio a 2-1 lead over the NBA champion Miami Heat in the best-of-seven finals series.
"I don't know, I have no idea. We'll do an MRI tomorrow and hopefully it's nothing big and it's just a little cramping or it got tight on me," said Parker, who contributed just six points in the win.
The 31-year-old guard went to the San Antonio locker room in the third quarter and re-entered the game briefly in the fourth quarter before returning to the bench with the game's outcome all but decided.
The uncertainty about Parker's status for Thursday's Game Four in San Antonio dampened the mood on what was an otherwise raucous night inside the AT&T Center.
Danny Green and Gary Neal delivered career-best performances as the Spurs responded nicely from Sunday's 19-point Game Two loss in Miami.
The pair, each playing in their first NBA Finals, combined for 51 points for the Spurs, who are in the Finals for the first time since winning their fourth title in 2007.
Green had a game-high 27 points on 9-of-15 shooting, including seven three pointers, while Neal came off the bench to score 24 points on 9-of-17 shooting, including six from beyond the arc.
"It's been a while since I shot the ball like that. A couple of games in the season I shot it pretty well. But tonight it was totally different level of feeling - comfort level on the perimeter," Green said.
"I just kept running the floor, trying to get open. When I saw daylight, I would just let it fly."
The Spurs defense limited four-time league most valuable player LeBron James to 15 points on 7-of-21 shooting while his team mates were also unable to find their rhythm.
"LeBron missed some shots that LeBron makes," said Miami's Dwyane Wade, who had a team-high 16 points. "We can go back and look at the film, but I'm not worried about him at all.
"He'll make the adjustment. He'll be his normal great self."
San Antonio led by 11 in the first quarter but allowed Miami to get within six points by halftime.
The Spurs pulled away in the final two quarters with an array of shots that Miami were unable to answer as Green, Neal and Kawhi Leonard led San Antonio on a 13-0 run to open the fourth quarter.
"We got what we deserved," Miami coach Erik Spoelstra said.
"Every shot they wanted to get they got. We did not disrupt them. And then that's the flow. And it just went from there. We never got to our game."
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