The 32-year-old has been carrying several knocks throughout this summer's Test matches against Sri Lanka and India, including today's defeat at Lord's.
The Sussex player said in a statement: "I'm not doing justice to myself and more importantly the team and that is what matters first and foremost. 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.
"Playing for England is the greatest honour you can have in the game and that is my motivation to come back and try and play again in the best possible condition. I've made my decision for the good of the team and whoever comes in I genuinely wish them the best of luck."
Prior, who was dismissed for 12 runs in the second innings earlier today, has earned 79 Test caps for England.