Ben Duckett, who opened for England in last month's drawn two-test series against Bangladesh, drops down the order to replace Ballance at number four.
The 19-year-old Hameed, averages 48.50 in first-class cricket for Lancashire and has four centuries and nine fifties.
“Haseeb has impressed everyone so far on this trip,” England captain Cook told reporters, adding that they had yet to decide on their bowling attack as they start the five-test series.
“You wonder if a 19-year-old, coming on tour, will be overawed but he hasn't been at all. He has looked really good in the nets and the way he has gone about his business. It's obviously a very special day to pick someone so young.”
Hameed, whose family roots are in India, will become England's youngest ever opening batsman.
“He is incredibly unflappable. He looks a very good player of spin. He picks length well and uses the crease well,” Cook added of his opening partner in Rajkot.
“Stuart Broad bowled at him last summer and was almost straight on the phone to me saying how impressed he was with this guy.
“It's probably a year earlier than he would have thought. But to average 50-odd as an opener in division one as a 19-year-old is an incredible feat. I was nowhere near the player he is at 19.
“Of course, there will be some tough moments for him over the next few days of playing test cricket, but I think this guy can play.”
Ballance scored just 24 runs in four innings in Bangladesh while Duckett struggled in his first three innings before scoring a fighting 56 in Dhaka.
“I feel sorry for Gary,” said Cook. “They were tough conditions in Bangladesh and ultimately it's about how many runs you score.
“It's unfortunate for Gary. In his six test matches back, he hasn't quite scored the runs he would have liked to.”
Cook, who had scored three centuries in consecutive tests the last time England were in India, was confident Duckett would be able to adapt to his role in the middle order.
“He's a pretty unflappable character,” Cook said. “Historically he has played all his cricket in the middle order until the last year. He's comfortable batting anywhere.
“It's never ideal when you chop and change but he is a fine cricketer.”
Original source: Teenage opener Hameed to make England debut