Prior, under pressure for his place after a poor run of form with the gloves and the bat, has not retired from international cricket but at the age of 32 and with ongoing injury problems his future must be in serious doubt.
"I'm not doing justice to myself and more importantly the team and that is what matters first and foremost," Prior said.
"I tore my quad before the first test and my right hand has been beaten to a pulp, but the main issue is the Achilles.
"Now we have the time, I want to be pro-active about how we deal with it so I imagine that I'll have an operation.
"I've always said as long as I can do my job I will manage the pain and get on with it, but it has now got to the point where I can't do my job to the level I expect of myself."
Prior has played 79 tests since making his debut in 2007, scoring more than 4,000 runs including seven centuries at an average of 40.18.
His absence will be another blow for a struggling England team who have not won in their last 10 tests following the retirement of off-spinner Graeme Swann, the axing of leading batsman Kevin Pietersen and the unavailability of Jonathan Trott due to a stress-related illness.
Captain Alastair Cook is under enormous pressure but after the defeat by India in the second test left England 1-0 down in the five-match series, he said he would not be standing down from the job.
England one-day wicketkeeper Jos Buttler is likely to be drafted into the squad for the third test starting in Southampton on Sunday.
(Reporting by Ed Osmond, editing by Mark Meadows)
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