Hamilton was never in the lineup during the series in Baltimore as he tried to recover from a pinched nerve in his lower back. The All-Star is expected to receive a second epidural injection of cortisone.
The Rangers start a series with the Indians in Cleveland on Monday.
"He's still day to day, and we hope to have him back for the Cleveland series," said assistant general manager Thad Levine before Sunday's game. "When is still to be determined. He'll be seen first thing [on Monday]."
Hamilton was expected to see Dr. Drew Dossett in Dallas to receive the injection, and it's not known whether he'll play in the Indians series.
"Realistically, opening day in Cleveland, he's not going to play," Levine said.
Hamilton did not travel with the Rangers to Baltimore but joined the team on Saturday. When he arrived, he was walking was a noticeable limp. After Saturday's 5-4 loss to the Orioles, he was moving much better, having received soft-tissue massages to relieve pain during the game.
"I slept last night, felt pretty good," Hamilton said on Sunday. "After the first 10 minutes, all of a sudden, I started aching and hurting."
Hamilton exited Wednesday's game with the Blue Jays after hurting his back sliding into second base during the fourth inning and received his first shot the following day.
"The shot doesn't get dispersed all over," Hamilton said. "It's just one local area. If it gets around the spot, I'll be able to tell, because it will be instantaneous pain. They shoot medicine in, and it kind of numbs it up."
Hamilton does not know how long the injury will keep him off the field.
"I might play in three weeks," he said. "I don't know. I might not feel better at all."
Hamilton skipped the team flight to Baltimore because the pain in his pinched nerve was too great. He said that the soreness is focused in his right leg and that he can't stand on one leg or put any pressure on it.
Manager Ron Washington will not rush Hamilton back.
"He's not going to come in here and say, 'I'm close,' " Washington said. "He's going to have to come in here and say he's ready. That's why we have those other guys out there doing the job. When he says he's ready, he's back out there. It's not going to be 'I'm close,' and then I'm tempted to put him in there."
Matt Palmer is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.