Richt would not discuss the reason behind the suspensions, only that a violation of team rules occurred. "They didn't do things the Georgia way," he said.
But a source told DawgNation that the three players were disciplined for failing a drug test that was administered last week before Georgia's 24-20 victory over Southeastern Conference archrival Florida in Jacksonville.
The source had no knowledge of when the test results were known.
Crowell, a true freshman who had 18 carries for 81 yards against Florida, is the team's leading rusher and ranks fifth in the SEC with 689 yards on 146 carries.
Thomas, a junior who is listed second on the depth chart, is the Bulldogs' third-leading rusher, with 200 yards on 44 carries. He carried only four times for two yards against Florida.
Malcome, a redshirt freshman who considered leaving the team earlier this season over a lack of playing time, has appeared in only one game. He had one carry for no gain against Coastal Carolina.
Three suspensions at the same position will leave Georgia incredibly thin. Moreover, second-leading rusher Richard Samuel (240 yards on 73 carries), who had a season-high 58 yards against the Gators, suffered an ankle injury on the final play of the game. Samuel had surgery Tuesday to repair the damage and will be out for four weeks, Richt said.
The next running back on the depth chart is redshirt sophomore Brandon Harton, who had 11 carries for 33 yards against Coastal Carolina in his only action this season.
When asked whether Harton would be the starter, Richt said, "I don't know about that. We'll kind of see how it goes, but everybody else who resembles a running back will be competing."
Cornerbacks Brandon Boykin and Branden Smith, both of whom have made appearances on offense in the past, could figure into the mix, Richt said, but New Mexico State's pass-heavy offense might limit their availability.
"Those guys will probably be on the field every single snap defensively, so we're going to need them to be fresh there," Richt said. "I don't know if there will be a huge difference in the amount of reps that they would get, but every week we spend time with them and have things ready to go.
"Sometimes we call them, sometimes we call a certain percentage of them. We may end up calling more of them in this game possibly."
Fullbacks Zander Ogletree and Bruce Figgins have yet to carry the ball this season and the remaining running backs on Georgia's roster are all walk-ons, including Wes Van Dyk, who rushed once for one yard against Coastal Carolina.
"It's an opportunity for us to change some things up and maybe
do some things differently and figure out ways to move the ball,"
Offensive coordinator Mike Bobo said after Tuesday's practice. "Other guys have got to step
up and make plays."
Georgia associate athletic director Claude Felton said Tuesday
athletic association policy strictly forbids a suspension being
delayed so a student-athlete can compete in an important game.
"Our athletic association regulations are firm that competition
suspensions, as a result of a violation of team or athletic
association policies, are immediate and occur at the next scheduled
competition," Felton said.
DawgNation writer David Ching, ESPN.com's Mark Schlabach and The Associated Press contributed to this report.