Finn took four wickets in a warm-up game against Pakistan A last week and was expected to be named in the team for the match in Abu Dhabi which starts on Tuesday.
"It's a bitter blow for him, he's had a huge 12 months," England captain Alastair Cook told reporters. "Hopefully, he'll be right for the second test."
Cook will open the batting with Moeen Ali, leg-spinner Adil Rashid will make his test debut and fast bowler James Anderson returns to the side after missing the last two tests in this year's Ashes series win over Australia.
(Reporting by Ed Osmond; Editing by Amlan Chakraborty)
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