McCrary, 61, who died Tuesday, had been on life support since suffering cardiac arrest during the weekend, The Atlanta Journal-Constitution reported.
"We appreciate the sympathy and prayers for the family -- that goes a long ways," Phil McCrary said in announcing his brother's passing.
The Falcons had picked McCrary out of Clark Atlanta in 1975 in the fifth round. He played with the team until 1977, going to the Washington Redskins in 1978 and then to the San Diego Chargers.
He retired from the NFL in 1981, having played in 74 games and making 13 starts.