Tavares, who was in attendance for the Islanders' first win of the season, cleared his baseline test Monday and has been given clearance to skate.
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The 20-year-old center, who played all 82 games last season, will skate Tuesday and Wednesday and, if he feels well after those two sessions, might play Friday against the Penguins. The Islanders play their first road game Wednesday in Washington.
Despite the encouraging progress Tavares has made, the organization plans on treating the injury with the utmost care.
"Any kind of trauma that has even the hint of concussion, the second impact is usually the most concern," GM Garth Snow said. "We'll take our time. John has a long career ahead of him, so we'll do what is right for him and this organization."
Tavares suffered the injury late in the first period of Saturday's 5-4 shootout loss to the Stars after an open-ice collision with winger Adam Burish. Tavares seemed foggy after the play but was able to skate off the ice with trainer Garrett Timms. He did not return to the game.
Coach Scott Gordon said he spoke with Tavares after the game Saturday and that the 2009 No. 1 pick said he felt fine besides having a stiff neck.
"It wasn't a head shot, it was more of a whiplash thing," Gordon said before learning Tavares' prognosis Monday.
Regardless of the severity of the concussion, Gordon said the team wants to be prudent about following protocol to avoid any long-term damage.
"You can't fool your brain. You can't talk yourself through fighting through it. The brain's going to set off an alarm that says, 'You can't do this,' " Gordon said.
Tavares' injury is the latest in a series of serious blows suffered by the Islanders recently. Mark Streit and Kyle Okposo suffered significant shoulder injuries during the preseason and are expected to miss six months and two months, respectively.
Michael Grabner, claimed off waivers from Florida last Tuesday, replaced Tavares in the lineup and made his Islanders debut Monday. Grabner, who skated on a line with Doug Weight and Nino Niederreiter, had one shot in 13:12 of ice time.