Coach Bob Davie announced the suspension Tuesday and then confirmed Wednesday that it came after a criminal complaint, the Albuquerque Journal reported.
According to the complaint, Jones exposed his genitalia to a woman on campus. He has not been arrested.
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, was beaten out for the starting job in preseason camp by junior college transfer Brandt Hughes.
Jones played in the second half of the season opener after Hughes suffered a season-ending shoulder injury.