The youngsters – aged just two and three – lay flat as their father feared stray bullets could fly through their windows.
The shocking incident on the Manor estate was the first of two shootings on the streets of Sheffield in just a few hours.
Residents say they heard eight shots being fired by men in cars on Scotia Drive, Manor, at around 9.30pm on Tuesday.
And just three hours later at 12.20am yesterday masked men in a car fired shots at another vehicle on Longley Avenue West, Shirecliffe.
Mandy Barton, of Queen Mary Road, Manor, told how her son ordered his youngsters to lie on the floor to keep them safe.
The 49-year-old said: “My son, who lives on Scotia Drive, phoned me and said ‘Mum, something’s going off. I think there’s been a shooting’.
“He said that he told his wife and my grandchildren to lie on the floor in case any shots came through the window.”
“They’re only little – one of my grandchildren is two and the other one is three.
“I kept thinking, what if something happens to them?”
She added: “I heard seven or eight gunshots and then saw all these cars coming backwards and forwards.
“As soon as I heard the shots I ran to my children and got them to go into another room so they would be away from the window in case any shots came through.
“I was very scared for them.”
Queen Mary Road resident Katrina Fearn, 20, added: “Things like this are why I don’t want to go past my door.
“I don’t feel safe, in the day or at night. There’s still stuff going off at all hours.
“There’s so many teenagers starting fights and causing trouble. I hear them fighting outside my house at two and three in the morning.
“We don’t really see the police around here, I think I would feel safer if we did.”
A police spokesman said: “Police were called to reports shots had been fired in the Manor area of Sheffield.
“Resources were sent to the local area to establish the full circumstances of the incident.
“At this time, nobody is believed to have been injured.
“Officers believe there may have been an altercation between people known to each other and officers remain in the community carrying out enquiries.”
The spokesman said they do not believe the two gun crime incidents are linked.
He added: “Police were called at around 12.20am, when a car containing four men in balaclavas are reported to have fired shots at another car in Longley Avenue West after following it from Penrith Road.
“Following a search of the local area, a car believed to be involved was later recovered abandoned and on fire in Nestfield Way, Sheffield.
“Nobody was injured during the incident and officers remain in the area carrying out enquiries and providing reassurance.
“At this time, it is thought that the incident involves individuals known to each other but officers are keeping an open mind.”
n Anyone with information on either incident should call South Yorkshire Police on 101.