Dyer was recalled to the starting line-up for Swansea's 2-0 win over Leicester City on Sunday, but lasted less than 10 minutes before limping off.
A scan on Monday revealed that the 29-year-old winger had ruptured the Achilles tendon in his left ankle.
Former Southampton forward Dyer has featured in five games since Paul Clement was appointed Swansea manager last month.
(Editing by Robin Pomeroy)
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