The victim was killed on Thursday evening – the second fatal stabbing in the city this week.
A South Yorkshire Police spokesman said: “A teenage boy is currently in police custody in connection to the death of a 15-year-old boy in the Lowedges area of Sheffield.”
He added: “A 15-year-old boy from Sheffield is now in police custody where he will be questioned by officers on suspicion of murder.”
Police first received reports of the stabbing around 7.50pm on Thursday. The boy was taken to hospital but died an hour later.
Chief Superintendent Stuart Barton said police did not believe it was a random attack and “there may be a bit of targeting with it”.
The victim has not yet been formally identified, but his family has been informed.
An area remained cordoned off at the end of Lowedges Road on Friday, with a forensics tent beside the A61 Sheffield-Chesterfield dual carriageway.
On Tuesday night, 19-year-old Ryan Jowle was stabbed in the chest in the Woodhouse area of Sheffield.
He died the next day at the Northern General Hospital. An 18-year-old woman and a 24-year-old man were arrested on suspicion of murder.
The man is still in custody but the woman has been bailed.
Police in the city are considering additional stop-and-search powers after the two incidents.
“This weekend we’re considering some, maybe, additional powers that we may wish to use, that we don’t like to use on occasions, around stop-and-search,” said Chief Superintendent Stuart Barton.
“We get to some points when we think what more can we do, how can we support people, how can we give people that presence?”
He said any powers would cover “certain areas” rather than the whole city.