The collision took place in Moncrieffe Road, Nether Edge at around 9pm.
A spokesman for the council's Streets Ahead team said on Twitter: "There is debris and oil on the carriageway from an RTC on Moncrieffe Road, our ISU team are en route to attend, please take care."
The Streets Ahead team and emergency services are understood to have left the area at around 12.30am this morning, when the road was re-opened.
It is not yet known whether anyone was injured in the collision, or how many vehicles were involved.
Streets Ahead and South Yorkshire Police have been contacted for more information.