Chara participated in all of the early drills but exited midway through the hour-long skate and did not return.
"He's progressing and we'll make a decision depending on how he is tomorrow," coach Claude Julien said.
"It's very disappointing," Seidenberg said. "It's tough luck the way it happened, but in the end there's nothing I can do. It's all about getting it fixed now and preparing for next season."
Seidenberg will meet with team doctor Peter Asnis on Tuesday to determine when to schedule the surgery, depending on how bad the swelling is.
He suffered the injury after getting tangled with the Senators' Cory Conacher behind Boston's net. Seidenberg has dealt with MCL injuries in the past, but he knew right away that this one was different.
"I didn't know what it was but I felt a click, so we tested it out in the locker room and kind of knew what it was but didn't know until the MRI the next day," he said. "It was pretty painful, but right now it doesn't feel bad at all."
Former Bruins teammate and fellow German countryman Marco Sturm, who suffered a similar injury during his career, called Seidenberg on Sunday to offer advice.
"He talked to me about it and said he feels great right now," Seidenberg said. "He said he would have done it again, because there's always options of not getting the surgery done. He wished me the best of luck and it was nice talking to him."
Prior to Monday's practice, forward Loui Eriksson (concussion) skated on his own and is progressing, and defenseman Dougie Hamilton practiced with the team for the first time since suffering a lower-body injury on Dec. 8 at Toronto.
"He skated, just a light skate here to see how he's doing," Julien said of Eriksson. "These kinds of things are day to day."