The rider was unseated from the Kevin Ryan-trained Savannah Moon after his mount clipped heels and stumbled a furlong and a half from home.
Eaves, who fell into the path of several horses, initially went home after the incident but was taken to hospital for scans on Tuesday morning.
His agent Richard Hale confirmed the injury and said the jockey faces a extended spell on the sidelines.
Hale said: "He has broken his leg.
"He went for an X-ray this morning and has got three breaks.
"He went home last night, then he was in that much pain they took him to hospital first thing this morning.
"He's having a full pot on his leg, so it will be a long job. He'll be out for the rest of the season anyway."
Eaves has enjoyed Group 1 success on top sprinters Brando and Tangerine Trees in recent years.
Savannah Moon, who was a 10-1 shot for the Phil Eadon Allancia Handicap, emerged unharmed.
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