Police were called to the incident at Blynk on Chesterfield Road at 1am on Saturday (12 December).
South Yorkshire Police confirmed an investigation is now underway.
A spokesperson said: “Police received a call at 1am with reports of a vehicle reversing into a shop. Officers attended and a vehicle was recovered from the scene.”
Nothing has been reported stolen, police said, but “considerable damage has been caused to the shopfront.”
A picture posted on Blynk’s Instagram page also showed significant damage to the beauty salon’s interior.
A message alongside the post read: “Thank you so much for everyone’s kind msgs [sic], it really means the world to us right now”.
The business said it is looking for a new, temporary premises and will honour all deposits for bookings.
The Star has contacted Blynk for further comment.