The move came less than two months after Cunningham was charged with possession of marijuana following a traffic stop in suburban Philadelphia in which police said they also found a pellet gun in violation of a local ordinance.
Charlotte acquired the former Villanova player from Portland in a February trade that sent forward Gerald Wallace to the Trail Blazers. The Bobcats moved the 6-foot-8 Cunningham from power forward to small forward and he thrived, averaging 9 points and 4 rebounds in 22 games while showing a consistent mid-range jumper.
Before the final game of the season, owner Michael Jordan said they wanted to re-sign the 2009 second-round pick. But the franchise became more cautious following his arrest.
Radnor Township Police Superintendent William Colarulo said officers responding to a reckless driving complaint stopped Cunningham. He said officers smelled marijuana and recovered a suspicious substance after Cunningham consented to a search.
Cunningham was arraigned and released on bail.
President of basketball operations Rod Higgins said last week that they would wait until after the draft to decide on Cunningham's future. Then Charlotte swung a draft-night deal that sent top scorer Stephen Jackson to Milwaukee and left the Bobcats extremely thin at small forward.
The qualifying offer means the Bobcats can match any offer another team makes to Cunningham.
Higgins didn't immediately reply to a phone message Monday night seeking comment. But coach Paul Silas said last month showed support for Cunningham, who has participated in offseason workouts recently at the Bobcats' practice facility.
"Things happen and I just hope he learned from it and that certainly that will never happen again. At least that's my hope," Silas said. "Everybody makes mistakes and if he learns from his mistakes he'll be OK."