The team had already ruled him out of Saturday's game against the Toronto Maple Leafs.
Crosby practised with the team on Friday, taking part in various drills, though he did not take faceoffs or engage in contact, and noted that being able to do both of those was a mandatory hurdle to cross before a return could be considered.
The wrist surgery, Crosby's second in a bout a year, was done to address an issue that has ailed him since 2014, he revealed Friday.
"The first time I ever injured it was 7 years ago. (Ryan Reaves) got hold of me pretty good at home here after the Olympics," Crosby said. "It was something that I kind of had to manage since then, and was able to avoid having to do any surgeries or anything like that until last year.
"It was something I was always able to manage somehow in the summer, just being able to get rest. Then obviously during the year, it was something that would kind of come back and I would get through it. Then this year, it just wouldn’t come back over the summer."
The Penguins have started the season 2-2-0 despite the absences of Crosby and Evgeni Malkin, who will be sidelined until at least December as he recovers from left knee surgery. Bryan Rust is out, too, as he deals with a lower-body injury that the Penguins have characterized as a "week-to-week" issue.
Pittsburgh will also be without Jeff Carter against the Maple Leafs this weekend. The centre missed the last two practices after testing positive for COVID-19.
"It's still my understanding as of last night, he continues to be asymptomatic," Penguins head coach Mike Sullivan said on Friday. "He'll go through a certain protocol. It's fairly complicated because it involves county and state rules and regulations as well."
The Penguins did receive one piece of good news, though, with goaltender Tristan Jarry returning to practice after being placed in the league's COVID-19 protocols on Thursday.
"It was confirmed that it was a false positive," Sullivan said. "He had to go through a certain process the league requires from a protocol standpoint. That's why he was in practice today. That's certainly a relief from our standpoint."