"Obviously, the program is shocked and extremely disappointed," coach Mark Few told a news conference before leaving to prepare for Saturday night's game against Saint Mary's. "We regret the far-reaching effect this has on our program and the university."
Heytvelt, 20, and Davis, 21, have told Gonzaga officials they are innocent.
The Bulldogs had a game Saturday night against Saint Mary's.
Both players were booked into Spokane County Jail for investigation of drug possession.
Cheney Police Commander Rick Campbell said the amount of marijuana was enough for only a misdemeanor, but that possession of mushrooms is a felony.
Prosecutors have until the end of Wednesday to file charges. The two were released shortly before 1 p.m., a jail spokeswoman said.
Police said they pulled the car over because its tail lights were not working. Campbell said officers smelled marijuana and searched the car, and the players were cooperative.
"It was close to midnight. They needed to have their lights on," Campbell said.
Heytvelt, a 6-foot-11 sophomore forward, is averaging 15.5 points and 7.7 rebounds per game and has been considered a frontrunner for West Coast Conference player of the year. Davis, a 6-9 freshman, is red-shirting this season undergoing arthroscopic surgery on his shoulder to repair ligament damage.
Gonzaga, often a tough team come tournament time, is unranked and having a mediocre year at 18-8. The Bulldogs beat Saint Mary's 60-49 on Saturday. The Bulldogs remain tied with Santa Clara at the top of the West Coast Conference at 7-2. Santa Clara was due in town Monday, followed by Memphis (No. 10 ESPN/USA Today, No. 8 AP) on Saturday.
Athletic director Mike Roth said the university is still gathering information about the arrests and that the pair will face the same disciplinary standards as any other students.
Information from ESPN.com senior writer Andy Katz and The Associated Press was used in this report.