Stanback, the team's leading scorer and rebounder, was charged with the misdemeanor after he was arrested May 13 near campus, and he tested positive for marijuana, according to toxicology reports.
He was ordered to pay a fine of $585, perform 40 hours of community service, attend DUI school and take part in a victim impact panel.
"I regret the decision that I made and I apologize to everyone who cares about UNLV and Runnin' Rebel basketball," Stanback said in a statement. "I made a terrible mistake. I have learned a lot about myself through this process and I hope people are willing to forgive me."
The 6-foot-8 Stanback, who averaged 13 points and 5.9 rebounds as a junior, will miss the Rebels' Nov. 1 exhibition game against Washburn and the Nov. 11 season opener at home against Grand Canyon.
"Chace is a quality person who has had an outstanding track record in three-plus years at UNLV," first-year coach Dave Rice said in a statement. "That said, he made a bad decision that negatively impacted our program. We can't have that."
UNLV suspended its leading scorer for the second consecutive season following an NCAA tournament appearance. Lon Kruger, who left in the offseason to become coach at Oklahoma, suspended guard Tre'Von Willis last year for four games -- two regular-season games and two exhibitions -- after Willis pleaded no contest to a reduced misdemeanor charge related to a domestic incident.
Stanback, 22, will be required to complete education and counseling programs and submit to random drug tests as a first-time violator of the athletic department's Drug Prevention, Education, Testing and Treatment Program.
"This is a case of a young man who has been a fine representative of our athletics department over the years, but made a bad decision," athletic director Jim Livengood said in a statement. "I support Coach Rice's decision about the punishment for the arrest. We're all disappointed in Chace's decision, but he knows we are here to help him grow from this. We believe that Chace is the type of individual who will learn and grow from this experience."
Diamond Leung covers college basketball for ESPN.com and can be reached at firstname.lastname@example.org.