Bail for Sullinger, 21, was set at $5,000 after his plea on charges including assault and battery and intimidation of a witness. He is next scheduled to appear in court Sept. 19.
Later Tuesday, Sullinger released a statement through the Celtics in which he apologized and called the experience "humbling and embarrassing."
"I know that this situation has brought both sorrow and embarrassment to my girlfriend, my family, the Boston Celtics organization, my teammates and my fans," he said. "To all of you, I apologize from the bottom of my heart."
The Celtics also released a statement Tuesday afternoon, addressing Sullinger's arrest.
"The Celtics were disappointed to learn of the allegations against Jared and are currently gathering more information on the situation, which we are taking very seriously," the statement said. "We will reserve further comment until such point that we have sufficient additional information."
Police say officers were called to Sullinger's residence Saturday evening by his girlfriend, Deann Smith. She told them that earlier in the day Sullinger had assaulted her after she accused him of cheating on her and began packing.
"During this heated argument in the bedroom, Jared pushed her down onto the bed and got on top of her," Waltham police wrote in a report. "Deann states she tried several times to get up, but he kept pinning her down and would not let her up."
The report said Sullinger later threw Smith to the floor and wouldn't let her up.
Smith told police that Sullinger grabbed her phone after she threatened to call police and then left because he was scheduled to fly to Ohio. She told police she called them only after she knew Sullinger was out of state.
Police said Smith still had red marks visible on her chest when she spoke to them.
Police issued a warrant for Sullinger's arrest and he turned himself in at about 6 a.m. Tuesday.
Sullinger's attorney, Charles Rankin, said in court that Sullinger and Smith were "long-time sweethearts" who met at Ohio State. He told the judge that Smith waited 10 hours before calling Waltham police for help.
The Celtics selected Sullinger with the 21st pick in the 2012 draft. He vaulted into the starting lineup early in his rookie season before a back injury forced him to undergo surgery in early February, ending his season.
Sullinger has spent much of his summer rehabbing in Boston and is projected to be a key contributor on this season's team.
Information from The Associated Press was used in this report.