The council said Rev. Joaquin Hernandez Sifuentes was a parish priest in the northern state of Coahuila, which has been plagued by drug cartel violence.
It's unclear if foul play was involved in his disappearance, but the council said that "crime and violence destroy the most sacred thing we have, life."
Hernandez was supposed to take a short vacation from his duties beginning Jan. 3, according to the Saltillo Diocese. But a close friend was unable to reach him by phone that day.
Early that same morning, a neighbor saw two young men take Hernandez's car, but did not see the priest with them.
The friend went to the priest's residence at the church and found his room a mess, with closet and drawers open and clothes on the floor, unusual for a priest who was very neat and orderly, the diocese said.
Two days later the friend returned to the priest's residence and noticed that his suitcase packed with clothes and other belongings was still there along with the glasses that he needed to drive.
Among his possessions that were missing were his car, cellphone, tablet and computer.
Hernandez was ordained in 2004 and served in several churches before arriving in his current post on the outskirts of Saltillo in 2014.
Several Roman Catholic priests have been attacked in Mexico recently.
Three priests were abducted in the Gulf coast state of Veracruz in late 2016; one was found alive, and two were found shot to death.
Another priest was killed in the western state of Michoacan in September.
At least 31 priests have been slain in Mexico since 2006.