The Albuquerque Journal reports Lobos coach Bob Davie confirmed Wednesday the suspension came after a criminal complaint.
According to the complaint, Jones exposed his genitalia to a woman on campus. He has not been arrested and no phone number was listed for him.
The suspension comes as New Mexico (2-5) seeks to try to snap a four-game skid in their homecoming game against Hawaii (4-3) on Saturday.
Jones, who started seven games last year when New Mexico went 3-9, lost the starting job in preseason camp to junior college transfer Brandt Hughes.
Jones played in the second half of the season opener after Hughes suffered a season-ending shoulder injury.