An official of foreign ministry told that the Ambassador died of respiratory problems.
He was under treatment at the hospital from February 13, he added.
Earlier, he was appointed as the Bangladesh High Commissioner in United Kingdom.
Quayes also had served as a Foreign Secretary in the Ministry during 2009-12.
Quayes was a recruit of the 1982 batch of BCS foreign service cadre.
He had also served as ambassador to the Maldives and Russia. As a junior diplomat, he had worked in Bangladesh missions in Tokyo, Singapore, and Geneva.