"Intelligence and Cabinet work allowed the Attorney General's (AG) Office in the capital to secure the arrest of a man implicated in the homicide of two priests in Veracruz," the AG office said in a statement released yesterday.
According to Fox News Latino, the suspect was caught along with another individual on 13 October after committing the armed theft of a Nissan Versa car in the capital.
Soon after the robbery, the pair were caught by security officials, the AG office said.
After the car theft was immediately reported to police, officers began a search for the vehicle along with the car owners.
The suspects were "recognised and fully identified by the victims" of the car theft, and during the investigation of the case, it was found that "one of those implicated also had an arrest warrant pending against him," the AG office said.
The two Catholic priests and their driver were killed on 19 September after being kidnapped from the Poza Rica church.
On the same day it was announced that a "probable perpetrator" of the murders had been identified.
The Catholic Church in Mexico has expressed anger at the way in which authorities appeared to smear the slain priests with claims that they had been drinking with the perpetrators.
Church figures have said that organised crime is likely to be behind the killings.
Some 31 priests have been killed in Mexico since 2006.
A third priest, Fr Jose Alfredo Lopez Guillen, was found shot dead on a highway in western Mexico late last month.
The US State Department wrote in its 2015 International Religious Freedom report that priests in Mexico are "victims of extortion attempts, death threats and intimidation by organized criminal groups".