The 13-year-old was stopped by a man in West Drive, near Tooting Bec Common, and was forced into the woods before being assaulted.
The man is described as white, aged approximately 20, about 6ft tall with a slim build, dark eyes and was clean shaven.
Police have stepped up patrols in the area to provide reassurance following the attack on Thursday evening.
Det Insp Keith Ward said: "This was a horrific attack on a vulnerable young girl who was forced by this man into a secluded area and raped.
"The victim was able to provide a very good description of her attacker and we are keen to catch him before he has the opportunity to strike again."
The rapist was wearing a tracksuit top and bottoms with three white stripes down the sides, black trainers and a black woolly hat with black gloves when he carried out the assault.
A teenage girl has been raped in a woods in south-west London.