Michael Schumacher was skiing at a moderate pace at the moment of the accident which has left him in coma, news magazine Der Spiegel reported on its website on Saturday, citing a video filmed by a German witness.
The witness, a 35-year-old steward, said that he was filming his girlfriend with a smartphone when he captured by chance the moment when Schumacher hit his head against a rock in the French alps.
According to the witness, who contacted the German magazine on Friday, Schumacher was descending the slope at a "leisurely" pace - "a maximum speed of 20 kilometres an hour".
In the background of the film, a skier could be seen descending on an unmarked run between two groomed pistes before falling.
Der Spiegel said the witness planned to provide the video to French investigators.
Schumacher was skiing off piste on December 29 near the Meribel ski resort with his 14-year-old son Mick and friends when he struck a rock so hard that his helmet was split in two.