Brinkley (undisclosed) was placed on injured reserve Monday, Tori McElhaney of the Falcons' official site reports.
Brinkley was expected to take over as Atlanta's long snapper in 2022 following the departure of Josh Harris to the Chargers. The 32-year-old has made 138 appearances over his first 10 NFL seasons, but the Falcons may opt to bring in a backup option if Brinkley's injury is considered serious.