Grant is one of a number of voices to criticise the playing surfaces in Gabon and he declared "five injuries so far have been down to the pitch".
The Israeli added: "The main actors are the players and we need to give them the stage to perform well.
"The organising committee should change the rules to let teams replace players who got injured due to the pitch."
Grant highlighted the problem facing Group D rivals Egypt, who have only veteran stopper Essam El Hadary available after injuries to Ahmed El Shenawy and Sherif Ekramy but under tournament regulations cannot call up another goalkeeper to their squad.
"Two of Egypt's goalkeepers got injured due to the pitch. It is not their fault and not fair to them," Grant said.
"We cannot change the pitch now so let Egypt bring in another goalkeeper. They cannot stay with one 'keeper, even if we have to play against them, it's not sporting."
Tunisia defender Syam Ben Youssef believes the playing surface in Libreville - one of four pitches being used in Gabon - is so bad that his side will have to change their style when they face Zimbabwe there for their final Group B match.
So far the Carthage Eagles have played both their matches in Franceville, which is seen as the best of the four pitches.
"Of course (it will affect us) I think we have technical players we like to play," Ben Youssef said.
"But it's usual for us to play in Africa on bad pitches so we have to win and not care about the pitch."
Burkina Faso midfielder Adama Guira is also unhappy with the state of the pitches - but resigned to it at the same time.
After the Stallions' 1-1 draw with hosts Gabon in Libreville on Wednesday, he warned that players need to be careful in the conditions.
"To be honest it is very hard to play on that kind of a field because you can't control your running and stopping so it's difficult," he said.
"But we are in Africa and we are Africans so we'll do our best for our country."
Pitches are just about thinking and having the money - Caf must think about it
It is not just the pitch at the Stade de l'Amitie in Libreville that has been criticised. Mali's Bakary Sako was less than impressed with the surface in Port-Gentil after his side's goalless draw with Egypt.
"The pitch is horrendous it's really tough to control the ball, to drive with the ball, everything is tough," said the midfielder who plays his club football for Crystal Palace.
"You have to be focussed 100% but it is the same for both teams so we have to get on with it."
It is a problem that is not confined to the Nations Cup according to Grant, who revealed he was taken aback by the pitches when he first arrived in Africa as Ghana coach in November 2014.
"Africa has great champions but you can't play on these pitches," he told BBC Sport.
"I think when I came to Africa the first thing I was very very surprised about - and not in a good way - was the quality of the pitches.
"That's why I admire the local league and the local players - they are paid $100 a month, sometimes they aren't even paid, and the pitches are not so good.
"Eighty-two per cent of the injuries are ankle injuries and they are giving everything. You see the passion, I admire them really. The next target should be good pitches."
Former Cameroon international goalkeeper Joseph-Antoine Bell believes the continent's governing body, the Confederation of African Football (Caf), must address the issue.
"If the game is not attractive because of the pitch it means something," he told the BBC's World Football programme.
"Pitches are just about thinking and having the money - Caf must think about it.
"Africa likes to be told 'oh you have tried', but its not about doing your best it's about being the best."
However, it does not appear as though Caf is going to take any action soon, judging by comments made by Khalilou Fadiga, a former Senegal international now on Caf's technical and development committee.
"Let the players not expect the pitches in Africa to be like those in Europe," Fadiga said on Friday.
Ghana coach Avrant Grant believes the poor pitches at the Africa Cup of Nations are damaging the players.