The incident occurred on Monday night at around 7.10pm near to the Spinney Corner Shop in The Spinney, Balby.
Jodie Southgate, the mum of one of the teens, says the girls were walking away from the shop when they realised that a black BMW, travelling very slowly, was following them.
The 41-year-old told The Free Press: "She told me that they looked at the car, which was full with about five men, and as they were walking they heard the window being wound down.
She added: "They carried on walking and they heard the door open and realised that two men had got out of the car and had started running after them.
"The girls started running back to our house in Grenville Road, which luckily is only about 300 metres away.
"They told me what had happened as soon as they came in, but when we looked we couldn't see anyone.
"I want other parents to know about what's happened, because it's very scary that this could happen in a well-lit street.
"I want to think that they only wanted to scare the girls, and that is all they wanted from them - but I can't know that for sure.
"Thank God the girls were together when this happened, if I could say anything to other parents it would be to make sure kids aren't walking about by themselves at night."
A South Yorkshire Police spokesman told The Free Press: "Police were called to reports that two teenage girls had been followed by the occupants of a black coloured BMW car on Grenville Road on Monday evening (8 February) around 7.15pm.
"Due to the suspicious circumstances, officers checked local CCTV but the car could not be traced. Anyone with information is asked to contact police via: 101 and quoting incident number 944 of the 8 February."
This incident happened just two days before two boys were reportedly approached by men in a blue BMW in Bentley yesterday.
Read the full story here.