Wims' outburst led to a brief brawl between the Saints and Bears.
Gardner-Johnson appeared to poke Anthony Miller in the face earlier in the game.
Bears head coach Matt Nagy said postgame that Wims' conduct was "completely unacceptable," according to Larry Mayer of ChicagoBears.com.
"We talked to him and told him that's not how things go here," Nagy added.
Mims, a seventh-round pick in 2018, has caught 25 passes for 236 yards and two touchdowns during his career.
The young wideout could face further discipline from the NFL.