In some cases the burnt bodies of victims have been left in the streets, drawing crowds.
Moke Mwayuma, whose brother was burnt alive after being accused of theft, deplored his death and said he was innocent.
"He is not a thief. What is his crime? We don't know. We found the fire over there, and he was burning in it," she said.
The M23-appointed vice governor of South Kivu province, Dunia Masumbuko Bwenge, said there had been "several cases" of vigilante attacks "driven by the behavior of a population that feels threatened by these criminals — these thieves who kill, steal, and also commit sexual violence."
M23 advanced into central Bukavu on February 16 after the army withdrew.
The M23 advance is the gravest escalation in more than a decade of the long-running conflict in eastern DRC, rooted in the spillover of Rwanda's 1994 genocide into Congo and the struggle for control of Congo's vast mineral resources.
Rwanda rejects allegations by DRC, the UN and Western powers that it supports M23 with arms and troops. It says it is defending itself against the threat from a Hutu militia, which it says is fighting with the DRC military