The forward was injured in Vancouver's 6-4 preseason win against the Ottawa Senators on Monday. He had three assists in the game.
"He misses [the start of] training camp, and then he's going to miss a little bit of time here, hopefully he's back for next week," Canucks coach Travis Green said. "It's unfortunate, but we deal with it and move on."
The 22-year-old agreed to a three-year, $17.625 million contract Sept. 16 after not attending the first six days of camp as a restricted free agent. He was injured after being hit face-first into the boards by Senators forward Chris Tierney at 4:06 of the third period.
Tierney received a two-minute boarding penalty. Boeser continued to play but left with three minutes remaining in the period.
"I'm hoping that he's not out that long," Green said. "First and foremost, we need him back, you are not going to replace a Brock Boeser. Am I upset he has a concussion? Yeah, I am, but it's going to happen in the game of hockey, and it does happen."
The No. 23 pick in the 2015 NHL Draft, Boeser had 56 points (26 goals, 30 assists) in 69 games last season. He has 116 points (59 goals, 57 assists) in 140 NHL games.
Defenseman Oscar Fantenberg also is in concussion protocol after he was injured Monday. The 27-year-old signed a one-year contract with the Canucks on July 1 after he had four points (two goals, two assists) in 61 games with the Calgary Flames and Los Angeles Kings last season.
NHL.com independent correspondent Kevin Woodley contributed to this report
