The team announced that Love would not return during halftime and said the big man was being evaluated for a concussion.
Multiple sources with knowledge of Love's status told ESPN that the next stage of the evaluation process won't be possible until Love has a night's rest.
"Tomorrow will tell us more," one source said.
Timeout was called with 6:58 left in the first quarter and Boston up 10-6. After being helped from the floor to the bench by point guard George Hill, Love retreated to the locker room for evaluation.
Several Cavaliers applauded how their fellow teammates stepped up after Love's exit.
"I think they responded exceptionally well," LeBron James said after the game. "Our second quarter, our guys that came off the bench -- Jordan [Clarkson], Jeff [Green], Kyle [Korver] and Larry [Nance Jr.] -- they just gave us a huge boost in that second quarter. That's the reason why we outscored them by 16 in that second quarter. It was just huge. We needed it, obviously, more than ever tonight with the situation that we were in."
Added Korver: "I think we all had to step up. We rely on Kevin for so much. He's been so good for us. I think Jeff Green stepped in, played a great game. Jeff's just so versatile. He's able to guard anybody. He knocked down some shots tonight, played really well. Larry came in and just gave us huge minutes. I think, I don't know what his stat sheet says he did, but I thought he really changed the game in a lot of ways.
"So, that's what you have to do when somebody goes down. You can't just plug somebody else in. It takes a collective effort."
During the 2016 NBA Finals against the Golden State Warriors, Love suffered a concussion in Game 2, causing him to miss Game 3 of the series.
The Celtics had some concern for Tatum as well, with Boston coach Brad Stevens saying after the game that while "every indication is he's fine," Tatum will continue to be monitored for concussion symptoms. Tatum played 39 minutes in the Celtics' Game 6 loss, registering 15 points, 3 rebounds and 2 assists.
Stevens noted how Love's absence changed things a bit for Boston defensively, but he also praised Cleveland's role players.
"We would guard, obviously, a little bit differently with Kevin in the game, but with the different matchups that they're playing and everything else, when they went small, I thought those guys all reacted very effectively," Stevens said.
The series is tied 3-3, with Game 7 scheduled for Sunday in Boston.