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.
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(Editing by Robin Pomeroy)
