Snyder said that Rubio will be evaluated again on Saturday.
"If he could of played, he would have," Snyder said. "But just wasn't able."
Rubio had dealt with soreness in his left hamstring in early April, causing him to miss a few games late in the season.
Rubio appeared to tweak it after making a behind-the-back pass to Rudy Gobert midway through the first quarter of Game 6. Rubio grimaced and limped a little before checking out of the game.
"It's a tough series and it caught up with him a little bit," Snyder said. "But hopefully he'll be alright eventually. We don't know the timeline."
Without Rubio, rookie Donovan Mitchell took over the Jazz offense, scoring 38 points on 14-of-26 shooting, including 22 in the third quarter on 8-of-10 shooting.
"Donovan's played some point guard this year where he's been the lead ball handler, but it's usually been in short spurts," Snyder said. "When Ricky went out, there's just some hesitancy that's a function of losing your point guard that early in the game, and we wanted to simplify in the second half and play to our strengths."
Over the first five games, Rubio averaged 16.8 points, 8.6 rebounds and 7.8 assists. In Game 3, he had a triple-double with 26 points, 11 rebounds and 10 assists.
Utah won the Western Conference first-round series 4-2.