The victim was stabbed last evening just 300 metres from where Drummer Rigby was struck by a car and hacked to death.
Scotland Yard said officers were called to Wellington Street - just around the corner from John Wilson Street where Rigby was killed - following reports of a stabbing yesterday.
In the latest incident, the man sustained non-life threatening stab wounds to his chest and arm, and was subsequently taken to a south London hospital for treatment.
There was nothing to suggest the stabbing was related to the death of Drummer Rigby, sources said.
More From This Section
"We are working on the basis that the stabbing is not linked with anything to do with Wednesday," the source said.
The stabbing comes after the family of Drummer Rigby, 25, visited the exact spot of his murder and added to a sea of floral tributes at nearby Woolwich Barracks.
Counter-terrorism police made their ninth arrest over his murder yesterday, while the two main suspects remain under armed guard in hospital.