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.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Reporting by Ed Osmond; Editing by Amlan Chakraborty)
