It depends on what you consider most injured.
Using players on IR as the numbers, statistics from 2006-2009:
Linebackers has been the position to put most players on the IR in the years in question. This is due to having the most players on the field at one time (3.5 on average) and also being a significant part of special teams.
However, RB is the position that is most likely to suffer injury. They put 150 players on the IR from 06-09, but only account for 1.5 players on the field at any given time.
At the other end of the spectrum, QB is the least injured player on the field.
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