Hennessy started in Sunday's 20-17 loss to the Los Angeles Chargers as a fill-in for Elijah Wilkinson, who was placed on IR last week with a knee injury. Another left guard, Jalen Mayfield, already is on IR.
Hennessy, a third-round selection from Temple in the 2020 draft, started two games at center as a rookie.
Colby Gossett played behind Hennessy against the Chargers and could start in Thursday night's game at Carolina.
The Falcons also signed safety Jovante Moffatt to the 53-man roster from the practice squad. Moffatt played in the past two games on special teams as a standard practice squad promotion.
Outside linebacker Quinton Bell and offensive lineman Jonotthan Harrison were signed to the practice squad. Cornerback BoPete Keyes was released from the practice squad.
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