A 75-year-old man died after a stabbing at a house in Deodar Road just after 3.30am today (January 24).
Officers attended along with the London Ambulance Service which treated a man for stab wounds.
He was pronounced dead at the scene shortly after.
A 30-year-old man, who is thought to be known to the victim, has been arrested on suspicion of murder and remains in police custody.
A police cordon is still present on the quiet residential street behind which a forensics team is working.
Although formal identification has not happened, his next of kin have been informed and a special post-mortem examination is due to take place today.
Meanwhile, police enquiries remain ongoing and they have appealed to the public for help.
Detective Superintendent Amanda Mawhinney from the South West Command Unit which covers Putney said: “We are currently supporting the family of a man who was sadly killed in the early hours of this morning.
“I am aware that people in the community may feel shocked following this – we believe this to be an isolated incident and there is no wider threat to the public.
“Although we have made significant progress by making an arrest, I would like to make it clear that our investigation does not stop here.
“We need the local community to help us understand what happened in the early hours of this morning.
“We are appealing for anyone who was in the area at around 3am and that saw or heard anything unusual to contact us as soon as possible.
“You may notice a higher police presence within the area today whilst we carry out our enquiries.
“A scene is in place as well as road closures. If you feel the need to raise anything with our officers, then please feel free to speak with them whilst they are in the area.”
Anyone with information which could assist with the investigation is asked to call 101 stating CAD721/24JAN.
Alternatively you can contact the independent charity Crimestoppers anonymously on 0800 555 111 or by submitting an online form.