Afridi made his announcement to BBC Radio after leading Pakistan to a 150-run defeat in the first Test at Lord's here on Friday.
The batsman, out slogging for two on Friday, said he no longer had the temperament for the five-day game after what was his first Test in four years.
"I've not been fully fit with a side strain and so I will not play Test cricket after the match in Leeds," Afridi said.
Yawar Saeed, the Pakistan tour manager, told AFP: "Yes, he has told us he is not feeling comfortable with the injury and has told us he doesn't want to play (Tests) but we will talk to him and then decide."