The authorities are working on a plan of action to reduce tensions in the area as armed police are deployed on the streets.
Armed and unarmed officers have stepped up patrols around the Spital Hill area of Burngreave after a man suffered gunshot wounds and a teenage boy was stabbed during two mass street brawls within the last three days.
The force has also been issued with a Section 60 order giving officers additional powers to stop and search people for weapons.
Meanwhile, detectives are examining CCTV to try and identify those involved.
A South Yorkshire Police spokesperson said: "There is a significant police presence in the area while initial enquiries are underway and there will be an increased armed and unarmed presence in the community in the coming days to provide reassurance."
Gill Furniss MP has pledged to hold talks with councillors and police to see what can be done to improve the situation.
She said: "’I am shocked and dismayed by the incident which took place in Burngreave.
"I will be speaking to the police and meeting with local councillors to discuss the situation and how to move forward in reducing the tensions in the area and we will do everything we can to ensure incidents like these do not happen again."
Anyone with information about the alleged shooting or stabbing should contact police on 101.