"It's semantics to an extent," Melvin said. "Every cramp is a slight strain, based on hydration. We're hoping that's what it is."
Parker's status going forward is not immediately clear. He will be reevaluated in the coming days.
Parker had cruised through his first 3 2/3 innings before the incident, which occurred following his 48th pitch of the game.
"It was just something where I threw the pitch and it got tight on me," Parker said. "It happened so fast, I can't really tell you what happened. It's something we'll figure out in the next few days."
Parker tried to stay in the game, tossing a handful of warm-up pitches with Melvin observing nearby, but Oakland's skipper turned to Jesse Chavez in relief. Parker offered little protest to remain in the game, adding later in the locker room that "it probably wouldn't have been the smartest thing to try to gut through and stay there.
"We made a good decision."
Parker entered Saturday 4-0 with a 2.34 ERA and .176 opponents' batting average over his last six starts after beginning the year 1-5 with a 7.34 ERA and a .345 opponents' batting average.
Jeff Kirshman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.