The incident happened in Bramley Road, Ladbroke Grove at 7.35pm yesterday (February 14).
Officers and London Ambulance Service attended and found a teenager who had been stabbed.
He was taken to hospital for treatment where his injuries were assessed not to be life-threatening.
A boy was subsequently arrested on suspicion of conspiracy to commit murder.
He was taken to a west London police station where he remains in custody.
Police enquiries into the circumstances continue.
A spokesperson for Metropolitan Police said: “Police were called at 19:35hrs on Friday, 14 February to reports of a stabbing in Bramley Road, W10.
“Officers and the London Ambulance Service attended and found a teenager suffering stab injuries.
“He was taken to hospital where his injuries were deemed not to be life-threatening.
“A 13-year-old boy was subsequently arrested on suspicion of conspiracy to commit murder.
“He was taken to a west London police station where he remains in custody.
“Enquiries continue.
“Anyone with information is asked to call police on 101 or message @MetCC on X quoting CAD 6495/14FEB.
“Alternatively, you can contact the independent charity Crimestoppers on 0800 555 111 or visit crimestoppers-uk.org.”