Footage online shows at least nine police cars and two ambulances on the road, outside the Whitgift Centre.
One person wrote: "Croydon little girl has been stabbed in the neck on the school run bus."
Another tweeted: "Young girl stabbed on a school bus outside the #WhitgiftCentre in #Croydon. Traffic is chaos with #WellesleyRoad Northbound closed but I think the main focus should be on the child who has been harmed. Praying she survives."
The exact circumstances of the incident remain unknown.
Wellesley Road has been closed northbound.
Police at the scene
As many as 16 buses have so far been diverted because of the incident.
A witness on the number 60 bus to Streatham Station, who didn't want to be named, told the Sun: "Someone attacked a young girl.
"The victim was a schoolgirl, she must only have been about secondary school age. She was wearing a green school uniform.