Jackie Bradley Jr. was set to start in Ellsbury's place again, weather permitting. Ellsbury missed the first two games of the series Friday and Saturday.
Red Sox manager John Farrell said Ellsbury's injury has improved but he's not ready to play yet. After a day off Monday, the team hopes to have him back Tuesday night for the opener of a three-game series against the AL West-leading Texas Rangers.
Ellsbury stole a club-record five bases Thursday against Philadelphia. He entered Sunday leading the majors with 21 steals to go with his .337 on-base percentage and five triples. He has one home run and 20 RBIs.
Farrell also said outfielder Shane Victorino is not running full speed yet and it's "probably a little premature" to say he will go out on a minor league rehab assignment Monday or Tuesday.
"There's no issues when he's swinging the bat. It's just the acceleration, and obviously that's a big part of his game," Farrell said.
Victorino has been on the disabled list since May 21 with a strained left hamstring and it appears he won't be ready to be activated when he's eligible on Wednesday.
"He's not running at 100 per cent yet. The one thing that we're being cautious with here is that, based on the experience of having him come right back and play successive games and he's had a couple of setbacks prior to going on the disabled list, we want to be sure that there's a gradual improvement, which he's showing," Farrell said. "So we're just being, like I said, overly cautious given what's transpired."
Victorino has a .343 on-base percentage in 34 games during his first year with the Red Sox after signing a $39 million, three-year contract as a free agent in the off-season. The Flyin' Hawaiian also has two home runs and 10 RBIs.
"There's been no setbacks. There's been no re-aggravation of it. It's just a matter of when he tries to get to that explosiveness, he doesn't have quite the confidence, and we're honestly telling him to gradually get into it," Farrell said.
"What we don't want to do is turn this into an extended period. If it takes it a couple more days than the June 5 activation date, we're certainly willing to do whatever it takes to get by that. What we don't want to do is have that date be a drop dead date where all of a sudden he's back and then he re-aggravates it."