Andrus will return soon and, in the meantime, Texas will host the Houston Astros in the opener of a four-game series Thursday night at Globe Life Park in Arlington.
Houston will open the series by sending right-hander Gerrit Cole (6-1, 2.20 ERA) to the mound against left-hander Cole Hamels (3-5, 3.63).
Texas has won three of its last four games and heads into the series coming off an 8-2 rout of the Oakland Athletics on Wednesday when Jurickson Profar homered twice while Joey Gallo and rookie Ronald Guzman also homered.
While Texas was beating Oakland twice, Andrus began inching closer to returning from a fractured bone in his right elbow and his first career stint on the disabled list.
Andrus began taking batting practice and is hoping to start a rehabilitation assignment with Double-A Frisco as early as Monday. Andrus has been missing from the Rangers' lineup since April 11 but has been throwing without limitations and hitting soft-toss pitching.
"It's going really good," Andrus told mlb.com on Wednesday about his rehab. "We want to make sure we have no problems. I understand there is going to be soreness in the muscle and tendon, but as long as the bone is good, everything else is part of the process.
"I still need this week (of batting practice) to get my timing down," Andrus added. "I can do everything. It's about getting back to playing every day. I'm feeling good and getting better every day.?
Houston activated outfielder Josh Reddick from the 10-day disabled list on Wednesday and inserted him in the lineup in right field. He went 1-for-4 with a run scored in the Astros' 7-5 win over Seattle.
Houston has dropped seven of its last 11 games and is one game behind first-place Seattle for the AL West lead.
Reddick was originally placed on the DL on May 21 while recovering from an infection. He played in two games on an injury rehab assignment with Double-A Corpus Christi and went 4-for-8 for the Hooks, including a 3-for-4 performance on Tuesday.
"The toughest part of this injury was sitting around and doing a whole lot of nothing," Reddick said after Tuesday's game in Corpus Christi. "With the staph infection, it's just about sitting around and waiting for it to heal and close up.
"Baseball-wise, I didn't want to get out of shape. We were pretty constant on pushing the running game and all that stuff to make sure my legs didn't get tired for when I come back to the Astros."
Cole was the decisive winner in a 7-3 home victory over the Boston Red Sox on Friday when he allowed three earned runs in seven innings.
Cole has been tremendous in three starts against the Rangers in his career, racking up 34 strikeouts in just 21 innings against Texas. He is 3-0 with a 1.29 ERA in three career starts against the Rangers.
Hamels will be making his 13th start of the season. He leads all Texas starters in ERA, starts (12), innings (72.0), and strikeouts (74). He has gone 2-2 with a 2.89 ERA in last seven starts to lower ERA from 4.76 to 3.62, with the opposition batting just .199 against him during that span.
Hamels will be working on regular four days' rest after taking a no-decision in the a 3-2, 10-inning win on Saturday at Los Angeles.
He has gone 8-5 with a 3.95 ERA in 19 career starts vs. Houston, including 1-1, 2.55 in three starts this season.