Boss could be out for Sunday night's game against the Indianapolis Colts.
"We will go through all the tests," head coach Tom Coughlin said.
Coughlin said Boss also suffered a concussion last season and that "is one of the major concerns."
The Giants said Boss suffered it last year on Thanksgiving night at Denver but was cleared to play by the following Wednesday for the ensuing game.
Another concern for Coughlin is tackle William Beatty, who will undergo surgery to repair a fractured bone in his right foot. Coughlin said he didn't know how long Beatty will be out.
Beatty was forced to play a lot after Boss was knocked out of the game early, as the Giants only had one tight end in Travis Beckum. Beatty said he didn't know how he injured his foot late in the win over Carolina.
Coughlin didn't say whether the team will add another tight end off the practice squad. And he said he has not decided whether offensive lineman Shawn Andrews will play tackle to provide depth at that position with Beatty out indefinitely.
The coach thought Boss should have been aided by the new NFL rules designed to protect defenseless receivers.
"If people are following the rules, [Boss] doesn't get touched," Coughlin said. "Now we wait to hear what his status will be."
Special teams captain Chase Blackburn also suffered an injury to his MCL which he injured during training camp.
Cornerback Aaron Ross (plantar fasciitis) will practice this week.