Beckham beat Cassidy up before police arrived and arrested the alleged peeper.
Beckham, a former cornerback for the Tennessee Titans, chased after Cassidy and tackled him to the ground, holding him down until deputies with the Palm Beach County Sheriff's Office arrived.
The onetime defensive cornerback told deputies he saw Cassidy with his hands down his trousers "making a motion consistent with masturbating".
Beckham yelled at the stranger peering into his daughter's room, which prompted Cassidy to flee.
Beckham caught him at an apartment across the street.
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"I waited for a second, and I looked again", Beckham told the station, "and I see a white male, and he's standing by my window, and he's trying to get a better position".
When police arrived, a bloodied Cassidy claimed that his auto had broken down and that he was sitting in the bushes outside Beckham's residence waiting for the engine to 'cool down'. But he refused to say where the vehicle could be found.
Cassidy was then taken to a hospital, where he was diagnosed with a fractured cheekbone and eye socket stemming from his encounter with the former football player.
Geoffrey Cassidy, 48, was arrested Monday on a charge of lewd and lascivious exhibition.
Cassidy was being held at the West Detention Center on a $1,500 bond. He spent the first five years of his career with the Titans, who selected him in the fourth round of the 2002 draft.
Beckham spent five seasons in the National Football League as a cornerback for the Tennessee Titans and Detroit Lions.