The 21-year-old musician, who wishes to be known only as K or his stage name Kdogg, suffered serious injuries including a broken leg, nose and cheekbone after the attack in in Bristol on July 22.
He was deliberately struck by a car as he walked in Monks Park Avenue in Horfield, after finishing his shift at nearby Southmead Hospital.
Avon and Somerset Police said the incident is being treated as a racially aggravated attack due to racist language used by the two occupants of the car, who fled the scene.
The two 18-year-old suspects were arrested on Saturday morning and are currently in police custody, the force confirmed.
The vehicle involved in the incident has been seized and police are awaiting the results of a forensic examination that was carried out on it, a force spokesman said.
Police are continuing to take witness statements, complete house-to-house inquiries and ensure any available CCTV has been fully reviewed.
Superintendent Andy Bennett, of Avon and Somerset Police, said: “We appreciate this incident has caused a significant amount of concern but we’d like to stress there is no intelligence or information to indicate there’s a further risk to the public.
“If anyone does have any concerns or worries then I would urge them to speak to officers within their local neighbourhood policing team who will be happy to answer any questions they can.”
Supt Bennett added: “I know the senior detective overseeing the investigation has spoken personally with the victim to provide as much reassurance as she can and a dedicated contact officer continues to update him about the progress of the investigation.”
He said the force continues to work with community leaders, the local authority and the charity Stand Against Racism & Inequality (SARI), which is supporting K and his family.
“I’d like to thank the many members of the public who have shown their support either by providing us with information or making gestures of solidarity with the victim,” Supt Bennett said.
“Bristol is a wonderful city full of diverse communities and I continue to be heartened by its reactions to incidents such as this.”