The Hudspeth County Sheriff's Office says the jailbreak happened Monday night as three men overpowered two guards. A spokesman for the sheriff's office did not immediately provide further details early Tuesday.
Officials say a deputy suffered a shoulder injury in a wreck during the pursuit.
Hudspeth County, in far West Texas near El Paso, has gained attention in recent years for celebrity arrests in drug cases.
Singer-songwriter Fiona Apple was arrested last month for hashish possession. Country star Willie Nelson, rapper Snoop Dogg and actor Armand Hammer were arrested on marijuana charges in unrelated cases.