The Italian defender tried to prevent Shane Long getting to a cross and was hurt by the Southampton striker in an aerial challenge.
"He was spitting blood," manager Louis van Gaal told reporters. "It was not nice for the players to see that."
Darmian becomes the fifth United full back to join the injured list, joining Marcos Rojo, Antonio Valencia, Ashley Young and Luke Shaw.
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United's defeat left them fifth in the table, 10 points adrift of leaders Leicester City.
(Writing by Tony Jimenez; Editing by Pritha Sarkar/Andrew Both)
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