Wallace, a restricted free agent, has refused to sign his one-year tender. Until he does, the team has suspended negotiations on a contract worth $2.5 million.
Coach Mike Tomlin told the Pittsburgh Post-Gazette Wallace's decision was "unfortunate."
"One thing that experience has taught me is that this is bigger than all of us," Tomlin said. It's bigger than Mike, it's bigger than me, so I mean that when I say it's unfortunate for him that he's not here."
Emmanuel Sanders will replace Wallace in the interim.
Wallace was picked for the Pro Bowl last year, his third year with the team.
Attendance at training camp is particularly important this year, however, because the team has a new offensive coordinator, Todd Haley.
Sanders was confident his teammate would pick up the new system whenever he returned.
"It's definitely just [X's] and O's," Sanders said. "You don't get that experience you get being out here or in OTAs. But they'll give him his fair share of reps so he'll catch up with us."