Faulk, 36, had hoped to come back for a 14th season. His role was diminished last season because of his recovery from a 2010 ACL tear.
Faulk played in 161 games over 13 seasons.
A member of the Patriots' 50th Anniversary team, Faulk is the franchise's all-time leader in all-purpose yards (12,349), kickoff return yards (4,098), and receptions by a running back (431, which ranks fifth overall).
Tuesday's ceremony will begin at 10:30 a.m. It is open to the public, but those wishing to attend must purchase admission to the Hall. Half of the ticket proceeds from 10 a.m. to noon will be donated to the charity of Faulk's choosing.