Hall, in his sixth year, will be eligible to return to the active roster on October 3 after Tennessee's Week 4 game at Cleveland.
Titans general manager Mike Reinfeldt said the team had known "for some time" that Hall might be suspended and used the preseason to identify players who could fill the hole.
"Johnson is a traditional, downhill, blocking fullback who we think will fill that need," said Reinfeldt. "He is a former fifth round pick who has done a nice job over the last two years for Green Bay."
The Titans cut nine players before Saturday's deadline, including veteran wide receiver Justin Gage, and trimmed their roster to 54 players. It can remain there until the exemption for running back Chris Johnson is removed and they get down to the NFL's mandated 53-man roster.
The Titans also waived guard Ryan Durand, defensive end Pannel Egboh, injured wide receiver Yamon Figurs, defensive end Jacob Ford (injury settlement), safeties Robert Johnson and Vincent Fuller, injured cornerback Pete Ittersagen and cornerback Frank Walker.