TORONTO -- After missing the first two games of the series in Toronto with an illness, J.D. Martinez is experiencing some back tightness and has been held out of the lineup for the third straight day.

Red Sox manager Alex Cora is taking into account both the artificial turf at Rogers Centre and the fact that Thursday’s finale is an early start at 12:37 p.m. ET.

“We may have to stay away from him the next few days,” Cora said. “Shoot for Friday, hopefully, now. He’s in there now getting some treatment.”

The Red Sox are off to Houston for a three-game set beginning on Friday, and then they return home to Fenway Park on Monday for a three-game series against Cleveland. Over his first 44 games this season, Martinez has hit .308 with nine home runs and a .910 OPS.

Red Sox riding it out with Thornburg

Reliever Tyler Thornburg allowed two more runs in his one inning of work on Tuesday night in Toronto, raising his ERA to 7.71 on the season. Cora and the Red Sox have seen flashes from Thornburg, whose raw stuff has still impressed at times, but they are hopeful that their patience will be rewarded soon with more consistency.

“The most frustrating thing for him is that the stuff is there,” Cora said. “You see it, 94, 95 mph. He hasn’t been able to locate his fastball when he’s ahead in counts. He hasn’t been able to put people away. The breaking ball has been inconsistent. But he’s here and we’ve got to keep pushing.”

Rehab updates

Dustin Pedroia and Brock Holt will play in another rehab game on Wednesday with Triple-A Pawtucket.

“Most likely, Pedroia will go to Portland over the weekend instead of keeping going with Triple-A,” Cora said.

Double-A Portland is home for four games beginning on Friday, while Pawtucket is still on the road in Rochester.

Brian Johnson threw 1 2/3 innings on Tuesday for Double-A Portland, allowing three hits with a walk and four strikeouts. Cora expects that he’ll still need another couple of outings to get right.

“He was very inconsistent with his delivery, not consistent with the breaking ball, so we’ll see how he does in the next one,” Cora said. “We need him to be right. Physically, he felt better.”