Walsh was unable to compete in the Grand National after being thrown to the ground by Celestial Halo in the Aintree Hurdle earlier in the day.
The 30-year-old was taken to hospital and returned to Ireland that evening before visiting a surgeon on Monday.
"The arm is in plaster and he is going to be out for eight to 10 weeks," said his sister and agent Jennifer.
Irishman Walsh looked well placed on the Paul Nicholls-trained horse before crashing through the second-last hurdle.
Walsh was subsequently struck by Won In The Dark and was treated at the side of the course for several minutes before being stretchered off.
The County Kildare native was forced to miss his National ride on the hotly tipped Big Fella Thanks who, with Barry Geraghty on board, went on to finish fourth behind the Tony McCoy-ridden winner Don't Push It.
Even before Monday's prognosis, Irishman Walsh had already been ruled out of next week's lucrative Punchestown Festival, where Denman is likely to return for the Guinness Gold Cup.
Source: www.bbc.co.uk