Stevens made the trip to visit Andrew Smith, a center who played in the Butler Bulldogs' two national championship game appearances when Stevens was their coach.
Smith, 25, has been battling non-Hodgkin lymphoma. He was scheduled to undergo a bone-marrow transplant Thursday, according to The Boston Globe.
Assistant coach Jay Larranaga will serve as head coach for Boston on Thursday.
"We ask that the private nature of this visit be respected," the Celtics said in a statement.
Smith has been readmitted to the hospital amid a two-year battle with cancer, according to The Indianapolis Star. He was diagnosed with non-Hodgkin lymphoma in January 2014, according to the report.
Smith's wife, Samantha, asked for support Wednesday on social media.
Please pray. Pray so very hard. We need a miracle & Andrew asked me to have you all rally with us in prayer in this moment.
— Samantha Smith (@Samantha44Smith) January 6, 2016
Stevens reportedly visited Smith in November while the Celtics were in town to play the Pacers, two days before Smith was to receive a previous bone-marrow transplant.
"[Stevens] makes it very clear to our players on a day-to-day basis that family is the most important," Larranaga said.
Larranaga said he found out late Thursday morning he was filling in for Stevens and was not sure when Stevens would rejoin the team.
"It's a difficult situation for Coach Stevens and the people close to him, obviously," Larranaga said. "So we told him don't worry about what's going on here. We'll try to keep the ship going straight."
Larranaga said he reached out to his father, Jim, the men's basketball coach at the University of Miami, before Thursday's game.
"I texted with my dad real quick," Jay Larranaga said. "He told me, 'Don't talk to the refs.' That was his word of advice."
Information from ESPN staff writers Nick Friedell and Chris Forsberg and The Associated Press was used in this report.