Police sealed off Elizabeth Avenue in Kirk Sandall in the early hours of Saturday morning after a man was found laid in the road with serious injuries.
Eyewitnesses reported seeing the man bundled out of a silver car shortly after midnight, before the vehicle sped off.
South Yorkshire Police have confirmed that investigations into the incident are ongoing.
A spokesman said: “The man remains in hospital in a critical condition.
“A 37-year-old man has been arrested on suspicion of assault and kidnap.
“Enquiries are ongoing and anybody with information should contact the police on 101 quoting incident number 21 of the 12 June.”
On Saturday, one eyewitness said: “Young man 25-30s dumped out of a silver car and sped off. Beaten badly and bleeding but breathing.”