The Giants (2-9) announced the move Saturday, a day before they host the Green Bay Packers (8-3).
Colin Holba was signed off the practice squad.
The 35-year-old DeOssie, who rolled a PAT snap last weekend, has been the Giants' snapper since he was drafted in 2007. He and quarterback Eli Manning are the only remaining links to the team's Super Bowl titles in the 2007 and 2011 seasons.
This is only the second time DeOssie has missed games. He also went on injured reserve in 2015 with a wrist injury.
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