The Metropolitan Police said officers were called at around 7pm on Monday to an address in Bensham Lane following reports of an unresponsive woman.
The 30-year-old was pronounced dead at the scene.
Two 21-year-old men had been arrested on suspicion of her murder, police said on Tuesday.
The force said the men are believed to have been known to the woman and there was no threat to the wider public.
Local resident Mohamed Mughal, 54, told the PA news agency: “We didn’t see it (the incident) but last night we just looked out and the road was all cordoned off. There were lots of police cars, lots of ambulances.
“It was absolutely frightening.”
A police car remained outside the property where the incident is believed to have occurred on Tuesday night.
Mr Mughal, who lives on Bensham Lane, added: “It wasn’t on the street, it was inside the house.
“I think at 2am the police cordon was still there and the missus woke up at 6am and it was gone. We had forensics here earlier too.”
Asked if he felt the area was unsafe, Mr Mughal said: “This is Croydon, isn’t it?
“I’ve seen it down the road. I’ve seen a guy collapse right in front of us and all sorts of things.
“Being next to a major hospital has not made it safer.”
The woman’s next of kin have been informed, police said.
Chief Superintendent Andy Brittain, who leads policing in Croydon, said: “We are saddened to hear about the loss of this young woman.
“We are currently supporting her family while they process this shocking news.
“At this early stage, we believe that the two men were known to the woman and there is no threat to the wider public.
“Although we have made two arrests, we still need to have an understanding as to what took place last night in Bensham Lane.
“Did you hear anything unusual? Did you see anyone leaving the property? If you did, then please do the right thing and speak with us.”
Police appealed for anyone with information which could help the investigation to call 101 quoting ref: CAD 5952/20Jan.
