He was injured in a tumble from Cernunnos, for his boss JP McManus, at the final fence in the Summer Plate Handicap Chase won by Long House Hall.
Geraghty, 36, will see a specialist to determine whether he needs surgery.
"He'll be out for two to three months with that," said Irish Turf Club senior medical officer Dr Adrian McGoldrick.
The first big meeting in Ireland that Geraghty will miss will be the seven-day Galway meeting, which starts on 25 July.
Jockey Barry Geraghty will miss the Galway Festival and is out for at least two months after breaking his right arm in a fall at Market Rasen.