The PRI's reputation has been battered by graft scandals and Borge's arrest occurred in the midst of state elections on Sunday that showed the party's popularity on the slide.
The former governor of the state which is home to tourist resort Cancun had long been accused of corruption by opposition parties, although he has denied the allegations.
The attorney general's office said a warrant for Borge's arrest was issued by a Mexican court at the end of May on suspicion he had been handling funds of illicit origin.
In April, former PRI Veracruz governor Javier Duarte, who was one of Borge's contemporaries in office, was arrested on graft allegations in Guatemala at Mexico's request.
Duarte is still awaiting extradition from Guatemala.
Preliminary projections on Sunday showed the PRI had narrowly scraped home in an electoral race in one of its main bastions though it appeared to be heading for defeat in at least one other state it has traditionally dominated.
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