Conley suffered the injury during the first half of the Jazz's series-ending Game 5 win over the Memphis Grizzlies last Wednesday. He was a limited participant in Monday's practice before being ruled out of Game 1 Tuesday morning.
"Hopefully, we'll get him back as quickly as possible," Jazz coach Quin Snyder said. "But those things are hard to predict."
Conley, 33, an All-Star for the first time this season, has missed significant time due to injuries to both hamstrings during his two seasons in Utah.