If there's an upside, it's that the injury isn't considered serious, Green said Saturday.
Quackenbush suffered the injury during his first bullpen session Friday, which was the first workout for pitchers and catchers.
"He feels much better today," Green said. "We're going to hold him back to make sure he's ready to go."
That applies to veteran reliever Fernando Rodney, who suffered a slight left hamstring strain during the Caribbean World Series earlier this month. He indicated Thursday that the hamstring was at "85 percent" healthy.
The Padres are taking the cautious approach with Rodney, who will likely get the first crack at closing games.
"With bullpen arms, there's really no need to rush these guys," Green said. "… It takes five, six outings to get ready for the season. We're going to be cautious with those guys."
Other notes from Padres camp:
• The two players who haven't reported to camp -- left-handed pitcher Jose Torres and catcher Christian Bethancourt -- aren't far away from reaching Arizona, Green said. Torres, who is from Venezuela, was on his way to Peoria on Saturday morning. Bethancourt, who is from Panama, might not be far off from doing the same, Green indicated.
"We're excited about getting those guys in camp shortly," Green said.
• Andy Ashby, who pitched eight seasons (1993-99) for the Padres, is here in camp as a guest instructor. Ashby won 70 games and posted a 3.59 ERA over 187 games (185 starts) and won 17 games in 1998, the year that the Padres advanced to the World Series.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.