Police were called by the London Ambulance service shortly before 6pm following reports of a stabbing on Bourne Terrace in Paddington.
The teenager was taken to hospital for treatment, but his injuries are not believed to be life-threatening, the force said.
Police confirmed no arrests have been made.
A police cordon remains in place in surrounding areas while an investigation is carried out.
Westminster Police authorised the stop and search powers “to prevent further escalations of serious violence”.
Section 60 of the Criminal Justice and Public Order Act 1994 will be in place for 12 hours from 7.30pm on Wednesday, September 8 to 7.30am on Thursday, September 9.
It will cover Paddington, Maida Hill, Westbourne Green, and West Kilburn.
Anyone with information is asked to call police via 101 quoting reference CAD 5754/08Sep.
This is a developing news story, more to follow.