Fans must pay £90 for a Nike 'match shirt' identical to the ones that will be worn by players, while an adult 'stadium' England shirt is priced at £60.
Shirts for children aged between eight and 15 cost £42 with mini-kits priced at £40.
The previous Nike kit has only been available since last May - seven England matches - after the manufacturer took over from Umbro.
Grant said on Twitter: "On £90 England #football shirts for fans, it's not right. Loyal supporters are the bedrock of our national game - pricing needs a rethink."
Shadow sports minister Clive Efford said the price of the shirts was "disappointing" while QPR midfielder Joey Barton called it "appalling".
The Football Association said it avoids any involvement with kit manufacturers about pricing. Nike is selling other national team kits, such as Portugal's, for exactly the same prices.
"The FA is a not-for-profit organisation that puts £100million back into the game every year. It is through relationships with partners such as Nike that we are able to maintain that level of investment in football," an FA statement read.