Crosby skated in an individual workout first, then joined his teammates for the morning skate for the second time in four days.
The team announced at the time of the procedure that Crosby would miss a minimum of six weeks, but that mark passed last week.
The three-time Stanley Cup winner has been dealing with pain in the wrist off and on since shortly after the 2014 Olympics. He initially hoped offseason rest would give it time to heal properly, a strategy that worked for him during previous summers. But as training camp for the season loomed with symptoms still lingering, he opted to have surgery in hopes of fixing the problem for good.
The Penguins have been an early-season surprise without their captain, not to mention forward Evgeni Malkin. Despite their 5-1 loss to the Tampa Bay Lightning on Tuesday night, Pittsburgh is 3-1-2 with eight points.
But optimism is high for Crosby's return, and coach Mike Sullivan even joked Tuesday that he's confident the veteran forward will get his spot in the lineup back whenever he's finally cleared by medical officials.
As for Tuesday's game, the Penguins did appear sluggish, and the Stanley Cup champions made them pay. Ondrej Palat and Ryan McDonagh scored 10 seconds apart in the second period and the Lightning picked up their first regulation victory of the season.
A night after a loss to Buffalo that included giving up three goals in the third period, Tampa Bay had its most complete performance of the young season.
The Penguins will take on the Calgary Flames at home on Thursday.
"We have a lot of internal competition, because players are playing well," Sullivan said of the team's chemistry without Crosby. "We're playing collectively as a group, and our structure is good."
The Associated Press contributed to this report.