Siddiqui studied philosophy at Aligarh Muslim University and later studied chemistry at Frankfurt University, where he received his PhD in 1927. On return to British India, he worked at the Tibbia College Delhi and the Indian Council for Scientific and Industrial Research. He later moved to Pakistan and worked in the Pakistan Council of Scientific and Industrial Research. He went on to establish the Pakistan National Science Council and was appointed as its first chairman in 1961. In the same year he became a Fellow of the Royal Society. He later co-founded the Pakistan Academy of Sciences, and after retirement from the government, he founded the Hussain Ebrahim Jamal Research Institute of Chemistry.