Ojinnaka is suspended without pay for the season opener for violating the NFL's personal conduct policy.
He was arrested in May 2009 and charged with battery after his wife confronted him over his contact with a female friend on Facebook. He was accused of tossing his wife down stairs and throwing her out of the house.
Ojinnaka started five games at right guard in 2009. The Falcons bolstered their offensive line in the offseason by drafting guard Mike Johnson and center Joe Hawley.
The Patriots made another move Monday by releasing defensive back Terrence Johnson, who signed April 29 as an undrafted rookie free agent from California (Pa.).