The news was announced hours before the start of the Lobos' game against Houston Baptist at the Pit, which New Mexico won 107-88.
"Carlton Bragg and JJ Caldwell will not participate in today's game versus Houston Baptist," the statement said. "They are being withheld from competition and team activity until further notice. The athletic department has received information that requires further review. In the meantime, there will be no additional comments from anyone at UNM until that process is complete."
New Mexico is off to a 12-2 start and is undefeated at home.
Bragg, a team captain, transferred from Kansas in January 2018 and is averaging 13.7 points, 10.8 rebounds and 1.4 blocks this season. Bragg originally transferred to Arizona State but left for New Mexico without playing a game for the Sun Devils.
Caldwell leads the Mountain West in assists at 5.7 per game, and averages 5.8 points per game.
The short-handed Lobos, led by Corey Manigault with 21 points, struggled on defense in the first half but used a 26-2 run to put the game away.