Prior's decision came after England suffered a crushing 95-run defeat at the hands of the visitors.
The wicket-keeper batsman said he tore his quad before the first Test and apart from a hand injury an Achilles problem has forced him to take the decision.
"As it stands now, I'll miss three Test matches, and then I'll do my utmost to get fit and ready for the back-end of the winter. It is a huge decision and not one I have taken lightly obviously, because I could have played my last game," Prior said, announcing his decision.
Prior, who will undergo a surgery on his Achilles, said injuries have made it impossible for him to perform well at the Test level but refrained from saying that he would retire.
"I can't look too far ahead. Right now, I have to look at this series, and more importantly, the game starting on Sunday. I have to be very honest with myself, my teammates, coach and captain. I just don't believe I was able to perform at the level I expect of myself and the level I want to perform for England, with the injuries I'm carrying at the moment," he said.