The Islamic Foundation, an autonomous government agency, issued the fatwa over the weekend, saying devotees must instead use prayer mats.
But the move has attracted criticism both from within the government and Muslim clerics.
Prime Minister Sheikh Hasina told a weekly cabinet meeting on Monday she was "stunned", according to media reports, while pro-opposition Islamic groups reacted with fury.
"We strongly protest this faulty and fictitious fatwa," said a statement issued by a group of Islamic leaders and clerics.
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Muslims in the conservative nation traditionally kneel on the floor to pray.
But in recent years most of the country's half a million mosques have allowed elderly and infirm worshippers to sit on chairs.
"They issued the edict by consulting with the traditions of Prophet Mohammed and his companions and practices over the centuries," the head of the Islamic Foundation Shamim Afzal told AFP.
Afzal said chairs spoiled the beauty of the mosques, and that there had been a similar move to ban them in India.