Ortiz, Chapa said, was picked up in the early hours along Interstate 35 in Laredo.
Authorities say a U.S. Customs and Border Protection agent in Texas has been arrested on suspicion of having killed four women and abducted a fifth.
Alaniz said investigators were still trying to determine a motive for the killings, and all the women in the case are linked to the sex trade. "Our community is safe from this killer", Webb County Sheriff Martin Cuellar said in a statement, adding that Ortiz would be formally charged later on Saturday.
The first victim was identified as 29-year-old Laredo resident Melissa Ramirez, whose body was found on September 4.
Officers were looking for Juan David Ortiz after a fifth woman escaped from him and contacted police, AP reported.
Mr Alaniz said the cause of death was similar in each case.
Authorities didn't immediately disclose the victims' names or nationalities.
Ortiz is a 10-year veteran of the Webb County Border Patrol.
A U.S. Border Patrol agent is in custody in connection with the killings of four women and the kidnapping of a fifth in Texas. He says all the women worked as prostitutes. "We value the release of timely information and we are making this notice public in order to remove any unnecessary fear in the community", the statement said.
"Out of respect for the victims' family and friends, we ask that deference and due process be given to the investigation so that all the facts are brought to light and they can receive the closure they deserve". Authorities say one woman Ortiz had abducted escaped early Saturday morning and she was able to alert authorities. They also said Ortiz is believed to have been working alone.
While it was not agency policy to comment on the details of an ongoing investigation, Meehan said, criminal conduct by CBP employees is not and will not be tolerated.