Andrus was scratched from the starting lineup before the Rangers' game Thursday against Cleveland because of sensitivity in his left arm stemming from the tattoo.
After having nine hours of work done on the tattoo the past two days, Andrus said it felt like his arm was "on fire" Thursday morning.
"Doing it in the offseason was probably the best idea," he conceded.
Will the tattoo force manager Ron Washington to implement a no-new-ink rule during the season?
"I hope not," Washington said. "But if that's what it does to you -- but Elvis has been working hard, and having another day is not going to hurt him."
The tattoo features a picture of his father with the words "In loving memory" and "Dad" surrounding the image. Andrus' father passed away in 1996.
Andrus will be back in the lineup Friday and Saturday before he leaves to play for Venezuela in the World Baseball Classic.
MLB.com's top prospect, Jurickson Profar, replaced Andrus at shortstop in Thursday's game against Cleveland, and he'll do so again during Andrus' stint with Venezuela, which could last until March 20.