The 23-year-old pulled up with the problem during the victory over the Latics at Wembley, limping off after just 16 minutes to be replaced by Chris Smalling.
And after watching the Red Devils secure their first piece of silverware this season courtesy of a brace from Robin van Persie, the Brazilian fears he may be set for a spell on the sidelines.
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"A hamstring - I could be out four, five weeks," he told reporters when asked about the severity of the injury.
Manager David Moyes was not quite as concerned, though, with Rafael having to miss the Premier League opener against Swansea on Saturday through suspension anyway.
"Rafa said that he felt his hamstring and in a game like this when you have an opportunity to make substitutes, it was fine," the Scot told MUTV.
"He is suspended for the first game of the season anyway, so in a way, I wouldn't say it doesn't matter, but it won't have an effect on what we do next weekend."