"There will be no further update on Tyler Wilson's status today," Smith said in a statement Friday.
Wilson took a shot to the head and was knocked out of the game on Saturday in a 34-31 overtime loss to Louisiana-Monroe.
He'd been listed as questionable all week. But the decision was made that he wouldn't play after he underwent additional testing on Thursday, sources said.
Arkansas radio personality Bo Mattingly first reported Friday that Wilson wouldn't play against Alabama.
Wilson, a first-team All-SEC selection last season, didn't practice with the team on Thursday after practicing on Wednesday. Smith had said Wilson was being "evaluated" and that he expected something to be decided by Friday morning.
This is not the first time Wilson has battled a head injury. He suffered a concussion in the second week last season but came back and played the next week.
Allen finished the game last week against Louisiana-Monroe. Mitchell, who moved to receiver this season, was Wilson's backup a year ago. The Hogs likely will have a package in for the Alabama game that will use Mitchell's running skills.
"Whoever plays, we're going to have to do a good job of executing and do our job," said Alabama coach Nick Saban. "It really doesn't matter what happened last week. I'm sure we're going to get their best game."
Information from The Associated Press was used in this report.