Police were called to the Gordon Enclosure at the racecourse following an altercation at about 5.30pm.
A 25-year-old man from Shoreham sustained facial injuries and a 24-year-old man from Pulborough suffered a fractured hand, according to police. Both men had attended the racecourse together.
A 23-year-old man from Amersham in Buckinghamshire, arrested on suspicion of assault occasioning actual bodily harm, has been bailed until 22 June pending further enquiries.
Anyone who witnessed the incident is asked to contact [email protected] or call 101, quoting serial 1079 of 21/05.
Alternatively, call the independent charity Crimestoppers anonymously on 0800 555 111 (www.crimestoppers-uk.org).
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