He was born in Kolkata in 1905, to Monimohan Mullick and Monomohini. His father had a deep interest in traditional Bengali music. He started his early training in Indian classical music under the tutelage of Durgadas Bandopadhaya. He studied at the Scottish Church College of the University of Calcutta. An important turning point in his life came when, after finishing his studies, he came in contact with Dinendranath Tagore, who was Rabindranath Tagore's great-nephew. This led to Pankaj Mullick's lasting interest in Rabindra Sangeet. Rabindranath Tagore, in turn, grew fond of him, and soon Mullick became known as one of the leading exponents of Tagore’s songs.
Tagore's song, Nemecche Aaj Prothom Badal became his first commercial recording, with the Kolkata-based Videophone Company in 1926, at the age of eighteen. This was the first of many albums which made him a household name in Rabindra sangeet.
He started his career with the Indian Broadcasting Corporation in Calcutta in 1927, the forerunner of All India Radio (AIR), along with composer R. C. Boral, where he contributed as a music director and artist for nearly fifty years.
He contributed in various capacities to Bengali, Hindi, Urdu and Tamil language films for 38 years, starting in 1931. He worked as music director to artists like K.L. Saigal, S.D. Burman, Hemanta Mukherjee, Geeta Dutt and Asha Bhosle. He acted with famous film actors like K L Saigal, P.C. Barua and Kanan Devi. Along with Nitin Bose and R.C. Boral, Mullick introduced playback singing in Indian cinema.
He worked with one of the early film studios, New Theatres Calcutta for 25 years.