Nelson was charged with one count of first-degree assault and one count of third-degree assault.
Nelson, 20, kicked 24-year-old Isaac Dallas Kolstad in the head while Kolstad was lying on the ground after being struck by another man early Sunday morning, according to a criminal complaint. Kolstad, 24, a former Minnesota State-Mankato linebacker, was in critical condition Monday with a severe head injury.
The complaint said witnesses described Nelson as being upset over attention being paid to his girlfriend.
A police sergeant who viewed surveillance video described Kolstad striking Nelson in the back, then moving away and being pursued and struck by an unidentified man. Police released video in hopes of identifying the man, who ran from the scene.
"Nelson pushes past others, approaches I.K. and delivers at least one kick to the left side of I.K.'s head," the complaint reads. "Sergeant Knutson noted that the video clearly shows that I.K. was defenseless as Nelson delivers the kick or kicks to the head."
Nelson appeared in court Monday wearing an orange jail jumpsuit, with his hands cuffed and his ankles chained. Afterward, his attorney, Jim Fleming, said it wasn't certain who caused Kolstad's injuries, suggesting the man being sought by police "threw a debilitating blow to the victim."
Fleming said Nelson "was not an aggressor in this situation."
Nelson posted bail and was released from jail Monday night, said a corrections worker who declined to give his name. Nelson's name was no longer listed on the Blue Earth County Jail roster.
Nelson was a top recruit when he came out of Mankato West as the state's Mr. Football in 2011, and spent much of his first two seasons as the Gophers' starter. He played in 11 games last season, but announced afterward that he would transfer to Rutgers and what he said was a more pass-friendly offense. He threw for 1,306 yards, nine touchdowns and six interceptions last season and ran for 364 yards.
Nelson would have two seasons of eligibility left after sitting out next season. A Rutgers spokesman declined to comment.
Kolstad played at Mankato East and spent two seasons at North Dakota State before finishing his career at Minnesota State.
His family issued a statement saying it appreciated the support it has received since the fight.
"We feel it -- Isaac feels it -- and we cannot express how important and helpful that has been," the statement said.
Sam Thompson, who played football with Kolstad, told The Associated Press he was with him the night of the assault but declined to comment about what happened.
But he said Kolstad graduated in December and recently started working at Fastenal, a local company. He described Kolstad as a leader on and off the field and "just a family guy" who has a 3-year-old daughter and whose wife is pregnant.
"His personality is one people wish they had," Thompson said. "He is just one person ... that people gravitate toward."
Steph Stassen, a graduate student who said she witnessed the assault, told the Minneapolis Star Tribune that the bars had just closed when "all of a sudden, this guy comes out of nowhere and sucker punches" Kolstad. Stassen and her roommate said another person, not Nelson, threw the punch, but that a man she later learned was Nelson then kicked Kolstad in the head "like it was a soccer ball -- just out of nowhere."
According to the criminal complaint, doctors are not sure Kolstad will survive.
Blaine Kolstad, Isaac's father, posted on caringbridge.org Monday afternoon that his son remains in critical condition. He added: "Please keep Isaac and all those involved in your prayers."
Sunday night, he posted that his son has had surgery to put a pressure gauge in his skull and may need additional procedures.
"He is currently in critical condition and fighting for his life," Blaine Kolstad wrote. "He is young and strong, but the battle he has in front of him is enormous. ... We do know that his brain did sustain permanent damage. We do not yet know to what extent and won't for many days. He is very sick. Please pray for Isaac and all of those involved."
Police released surveillance video of events surrounding the altercation and are asking for the public's help.
Nelson transferred to Rutgers after two years at Minnesota and will sit out the upcoming season per NCAA transfer rules.
Information from The Associated Press was used in this report.