The 18-year-old Brazilian sustained the injury in last weekend's league victory over Blackburn Rovers.
"Rafael is out for a month with a slight hairline fracture of his ankle," Ferguson told the club's website.
"It's a blow for the kid because he's been playing in all the games and he's done so well. He deserves to be in the final."
Ferguson confirmed he would keep faith with several of the fringe players who got the club to Wembley for Sunday's game.
"Darron Gibson and Danny Welbeck will both play and deserve to play," he said.
"Jonny Evans has hopefully recovered from Tuesday's (Champions League) match. He was feeling his injury towards the end of the game. Like Rafael he deserves to play in the final.
"Other than that everyone's fit. Gary Neville's in the squad, he's been training well for about a week and will travel with us. Anderson played 45 minutes in the reserves last night and he'll travel down with us."
Goalkeeper Edwin van der Sar is not expected to feature, leaving Ferguson to decide between Ben Foster and Tomasz Kuszczak.
"It's not an easy decision for me, it's something I'll have to mull over," he said.
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