Witnesses quoted by the Jornal de Noticias daily said the Brazilian player had lost control of his sports car in the early hours of Saturday on a local road near Braga in northern Portugal. The car hit a wall in a nearby field and caught fire.
"I thought he was dead. My brother dragged him out of the car, and we put out the flames before the entire car burnt down," one of the witnesses told the paper.
The car was a two-seater, but there were two other passengers in it, a Brazilian woman and another man, according to local police.
"The three were given medical discharge at the end of Saturday morning. They only had minor and superficial injuries. The young woman needed the most treatment, but only small things," the paper quoted a spokesperson at the Braga hospital as saying.
According to local police, the trio had been at a nightclub in Braga before the accident.
The paper also cited a source at Gestifute, Anderson's Portugal-based agents, as saying the player will soon return to Manchester to continue his recovery from a knee injury he sustained in February.
It is not yet known whether the player faces police charges for the accident.
The 22-year-old spent two years playing in Portugal for Porto before moving to Manchester United in 2007.