WFAA-TV, citing sources, reported that Jeffress was arrested on a charge of driving while intoxicated. Dallas County records show the 28-year-old pitcher was jailed at 5:13 a.m.
The Rangers issued a statement saying they were aware of the situation and were in the process of gathering information.
Jeffress has a 2.52 ERA and 27 saves in 56 games. He has appeared in nine games for the Rangers and has allowed four earned runs in nine innings.
He served a 100-game suspension in 2009 for a third positive drug test while in the minor leagues. He would face a lifetime ban for another positive drug test.
Entering Friday's play, the Rangers lead the American League West by 7½ games over the Seattle Mariners.