The injured list was a possibility, manager Dave Roberts said.
Corey Knebel was called into action to start in Price's place as Los Angeles made it a bullpen game with the division race dead even. Both teams began the day at 85-49.
"It was something he's been dealing with, but then it kind of came to a head more after his last start," Roberts said of Price.
Roberts didn't offer specifics on Price's condition, saying: "It's an arm thing and he's just kind of felt it. It's nothing that's going to be a big deal. It's kind of making sure that we don't let it become such. If it is an IL, it'd be a short-term deal."
The 36-year-old Price, who opted out of the coronavirus-shortened 2020 season, has one year remaining on a $217 million, seven-year contract he originally signed with the Red Sox in December 2015.