Byrd suffered a hamstring injury during practice Tuesday, Steve Reed of the Associated Press reports.
Byrd's injury was described as severe, according to head coach Frank Reich. He is expected to miss at least a month, which would put him in jeopardy of missing the team's Week 1 game against the Falcons. That is if he makes the 53-man roster, which was no guarantee for the veteran receiver, and perhaps this injury lessens his chances to do so.