The 317,000-person county is the largest of four counties to adopt such a measure in the state, where abortion itself is also illegal.
Lubbock County commissioners voted 3-to-0 on Monday on the measure, which allows private citizens to bring lawsuits against those accused of providing or paying for travel through unincorporated areas in the county related to an abortion.
The decision could impact county residents seeking abortions in nearby New Mexico, where abortion is legal.
Anti-abortion activists celebrated the decision as part of a wider campaign to elimination abortion rights across the US.
“These abortion trafficking ordinances really are the next stage in an abortion-free America,” activist Mark Lee Dickson told The New York Times.
Health providers condemned the measure.
“Texas already live under some of the most restrictive and dangerous abortion bans in the country yet anti-abortion extremists continue to push additional unnecessary, confusing, and fear-inducing barriers to essential healthcare,” Planned Parenthood of Greater Texas wrote in a statement.
Other Texas jurisdictions have postponed considering such laws.
The city of Amarillo on Tuesday postponed a vote on a travel ban.
No violations of abortion travel ban laws have been reported so far in the three Texas counties where such provisions were already in effect: Mitchell, Goliad, and Cochran.
Legal commentators have questioned whether such provisions are unforceable under federal law.
“May a state bar a resident of that state from traveling to another state to obtain an abortion?” US Supreme Court Justice Brett Kavanaugh wrote in a recent opinion. “In my view, the answer is no based on the constitutional right to interstate travel.”
A suit from Texas attorney general Kex Paxton accuses Planned Parenthood of defrauding Medicaid.