A source told ESPN's Brett McMurphy that Robinson was dismissed for repeatedly missing classes and meetings and for his "continued inattention to detail in everything."
Malzahn said he kicked Robinson, Auburn's top returning rusher, off the team Wednesday before the Tigers' first practice of preseason camp.
"He did not meet my standards or expectations of what it takes to be an Auburn Tiger football player," Malzahn said. "We're going to have zero distractions on this team this year. I've given him his release, and we wish him the best."
Robinson came on strong late last season and ran for 639 yards and three touchdowns. Leading rusher Peyton Barber left early to enter the NFL draft, and No. 3 runner Roc Thomas transferred to FCS Jacksonville State. Barber went undrafted.
The Tigers, who open Sept. 3 against defending ACC champion Clemson, added former Baylor signee Kam Martin this summer after he was granted a release from his scholarship.
Kerryon Johnson is now the most established back on the team. He ran for 208 yards and also returned kicks last season as a freshman. Johnson missed virtually all of spring practice recovering from shoulder surgery.
"We're very confident in him," Malzahn said. "He's put on about 20 pounds. He's a guy that we've recruited to be a marquee back. He's got a great opportunity now. He's in a good spot."
Malzahn also said that Kamryn Pettway, a converted fullback, will get a shot.
Receiver Marcus Davis said the team learned about Malzahn's decision before practice.
"Jovon is a great guy, great teammate and everything, but we just focus on what's best for the team," Davis said. "It's nothing I really sat down and thought about yet, but at the same time, if coach Malzahn thinks it's the best thing for the team, I'm pretty sure everybody's going to be on board with that."
Robinson had signed with Auburn in 2012 but was ruled ineligible after a guidance counselor admitted to creating a fake transcript. He transferred to Georgia Military College and was the 2013 NJCAA national player of the year.
He set junior college records for a season in rushing yards (2,387), touchdowns (34) and points scored (204).
"We all support Coach's decision," offensive tackle Austin Golson said. "No one player is going to be able to take down our team. I believe that we're going to respond well and just keep practicing. We have plenty of other options that will be able to help us out. I think we're all going to be fine."
Last season, Auburn opened camp with star wide receiver D'haquille Williams suspended. He never got going during the season and was dismissed after a bar fight. Auburn, which was the preseason favorite in the Southeastern Conference, stumbled to a 7-6 season.
Robinson's dismissal is perhaps the biggest story at the start of camp, along with the three-man quarterback competition among 2015 starters Jeremy Johnson and Sean White and junior college transfer John Franklin III. Johnson and White struggled much of last season.
"We're going to rotate each day who's going to be out there first," Malzahn said. "We're going to have equal reps. We have a good plan for putting them in competitive situations every practice. We will chart everything. We're hoping we can name a guy sooner rather than later but we'll give everybody an equal shot."
The Associated Press contributed to this report.