Goc suffered the injury when he was knocked into the boards during Thursday's loss to the Los Angeles Kings.
"I hate to say when you get an injury report and it's like this that it's good news, but it could have been a worse prognosis for him," Bylsma said, according to the Pittsburgh Post-Gazette. "It was probably good news that it's just three weeks at this point."
Goc has recorded two assists in 12 games since being traded to Pittsburgh from the Florida Panthers earlier this month.
The Penguins clinched their eighth consecutive postseason appearance with Friday's 2-1 victory over the Blue Jackets.