Salimuzzaman was born in Subeha (Barabanki District) near Lucknow on 19 October 1897. His father's name was Chaudhry Muhammad Zaman and his elder brother Chaudhry Khaliquzzaman was a distinguished All India Muslim League leader and one of the founding fathers of Pakistan. He received his early education from Lucknow, both in the Urdu and Persian languages, and soon developed interest in literature, poetry, and calligraphy from his father Sheikh Muhammad Zaman. He graduated in Philosophy and Persian language, from Muhammadan Anglo-Oriental College (that would later become Aligarh Muslim University) in 1920.
In 1920, Siddiqui proceeded to University College London to study medicine. However, after one year of pre-medical studies, he moved to Frankfurt University in 1921 to study chemistry. In 1924, he married his German classmate, Ethel Wilhelmina Schneeman. He received Doctor of Philosophy under the supervision of Julius Von Braun in 1927. During his college days in Germany in the 1920s, Germany experienced high inflation and he went through some hard economic times. In these tough times, Indias then eminent philanthropist Hakim Ajmal Khan used to send him Rupees400 every month. Many years later, as a successful scientist in Pakistan, Siddiqui repaid Hakeem Ajmal Khans kindness by dedicating his discoveries to him.
On his return, he established the Ayurvedic and Unani Tibbi Research Institute at the Tibbia College Delhi, under the guidance of Hakim Ajmal Khan. He was appointed its first director. However, soon after the death of Hakim Ajmal Khan, Siddiqui left the post. In 1940, he joined Indian Council for Scientific and Industrial Research where he worked until 1951 when he migrated to Pakistan on the request of Prime Minister Liaquat Ali Khan.