Hopkins had been listed as questionable for the Week 17 encounter on Sunday and he was ruled out on New Year's Eve after his injury flared up this week.
He will sit out a seventh game of the season for a Cardinals side that are out of playoff contention.
Hopkins missed the opening six games of the year due to a suspension for violating the NFL's performance-enhancing drug policy.
Andre Baccellia has been promoted from Arizona's practice squad in the absence of Hopkins.
The Cardinals confirmed on Friday that David Blough will be the starting quarterback against the Falcons.