The forward was placed on injured reserve before a 3-1 loss at the New Jersey Devils on Thursday.
"It's week to week, that's the best timetable I can give you to," Hakstol said.
Burakovsky was injured on his first shift of the Kraken's 4-0 loss at the New York Islanders on Tuesday. He played 21 seconds.
He leads Seattle with 39 points (13 goals, 26 assists) in 49 games. Burakovsky signed a five-year, $27.5 million contract with the Kraken on July 13 after winning the Stanley Cup with the Colorado Avalanche last season.
"Injuries are a part of it," Hakstol said. "You're going to go through these different scenarios. There is no perfect timing for an injury. They happen and everybody has to deal with them and you have to find your way through."
Justin Schultz returned to the lineup against New Jersey after the defenseman missed six games with an undisclosed injury.
"'Schultzy' is a huge part of our team," Hakstol said. "He does an awful lot for our group not just on the ice, but he's one of those guys in the room that's a real calm voice, always has a great perspective and has been really effective for us."
