A fifth man, aged 25, was arrested on Tuesday evening after a police chase in Peckham, the Metropolitan Police said.
The five suspects were charged on suspicion of attempted murder and were being held without bond, according to the department.
The news release did not say why the five were arrested in connection to Johnson's shooting.
"While the investigation remains in its early stages, these arrests show that progress is being made. However, I would continue to appeal to those who may hold information about the events that led to Sasha receiving her horrific injuries, or about those responsible, to do the right thing and come forward and speak to police," Metropolitan Police Detective Chief Inspector Richard Leonard said.
The Metropolitan Police appeared to dispute claims from activists that Johnson was the victim of a targeted attack because of her Black Lives Matter affiliation and political viewpoints.
"At this early stage work continues to establish a motive but there is nothing to suggest that Sasha was the subject of a targeted attack," it said. "At this time, police are also not aware of any reports of threats made against her prior to the incident."
The Metropolitan Police, in an earlier update, said officers were searching for "four black males" who were dressed in dark-colored clothing who discharged the firearm during the shooting incident.
Reports have said that Johnson still remains in critical condition at a South London hospital.
Johnson's left-wing Taking the Initiative Party wrote earlier this week that she had received "numerous death threats as a result of her activism."
Black Lives Matter activist Imarn Ayton, described as a friend of Johnson, told ITV that it’s likely that she was shot in an incident that was “more related to rival gangs” in the area.
“I do believe that it was a party and there was some type of dispute between two individuals or two gangs, and it was wrong place, wrong time,” Ayton noted, adding that she doesn’t “believe [Johnson] was the intended victim.”