Police were called to Glorious Goodwood after a man was reported to have been bitten on the face, Sussex Police said.
A police spokesman said officers were called to the medical area at around 3.40pm on Thursday but as the man refused to provide any details, no crime was filed.
In a separate incident later that day, police said two men were arrested following reports of a fight at the west entrance of Goodwood at about 7.45pm.
The spokesman added that a 45-year-old man from London and a 25-year-old man from Waterlooville were both issued with a penalty notice for being drunk and disorderly in a public place.
The internationally renowned Qatar Goodwood Festival, known as Glorious Goodwood, is taking place at the racecourse until Saturday.