The 18-year-old did not travel with the United squad for their UEFA Champions League last-16 tie with Inter Milan after picking up the knock against Blackburn last Saturday.
The ankle problem comes after the full-back only recently returned after nearly three weeks out with a hamstring injury picked up at the end of January.
The injury could not have come at a worse time for the Brazilian with the Carling Cup final just days away. However Rafael's absence could have opened the door for twin brother Fabio to step in for the Spurs clash.
With United already low on numbers at the back with Gary Neville and Wes Brown unable to stay fit this season manager Sir Alex Ferguson will be hoping his charge can recover quickly.
The youngster has been the revelation of the season at Old Trafford in a campaign that has seen him feature 21 times in all competitions.
DisappointedFerguson was understandably disappointed with the news but revealed that Rafael was in fact his only injury concern going into Sunday's final.
"Rafael is out for a month with a slight hairline fracture of his ankle," Ferguson told Sky Sports News.
"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.
"Darron Gibson and Danny Welbeck will both play and deserve to play, Jonny Evans has hopefully recovered from Tuesday's 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.
"I have got to wedge in all the players who all of sudden are desperate to play in the final.
"So we will have to wedge them in which is going to be hard."