The 24-year-old striker hit trouble driving to the Barcelona training ground in rain before the team flew to the northern city of San Sebastian for the match.
Catalan television TV3 showed images of a dent on the left front of the sports car, which was parked on the side of a road.
"He had a car accident but was not injured and was able to continue his trip," a source close to the club told AFP.
Earlier this week Spanish prosecutors asked for a two-year jail term and a 10 million euro ($10.6 million) fine on charges of corruption during his transfer from Brazilian club Santos to Barcelona.
However, Neymar will have to be on his best behaviour against Real Sociedad as a yellow card would see him miss next weekend's Clasico against Real Madrid through suspension.