Haku Shah was born in 1934 in Surat, Gujarat.

In 1955 he received his degree in B. F. A. from the Faculty of Fine Arts at M. S. University, Baroda. In 1959 he received his degree in M. F. A. from Faculty of Fine Arts, M. S. University, Baroda.

He had several solo shows:
In 1964 he had solo exhibitions at Academy of Fine Arts, Kolkata. In 1963 and 1964 he exhibited solo at Jehangir Art Gallery, Mumbai. In 1967, 1968, 1969, 1975 and 1994 he exhibited solo at Gallery Chemould , Mumbai. In 1967, 1992, 1993 and 1997 he had solo exhibitions in New Delhi. In 1968, 1969, 1976, 1991 and 1998 he had solo exhibitions in Philadelphia, San Francisco, St. Louis, New York, Berkeley and Cape Town. In 1971, 1981, 1982, 1997 and 2005 he had solo shows in Ahmedabad. In 1996, 1994 and 2014 he had solo shows at Cymroza Art Gallery, Mumbai. In 1998 he exhibited solo at the Lalit Kala Academy, Chandigarh. In 1998 he exhibited solo at Durban Art Gallery, Cape Town. In 1999 he exhibited solo at the AIFACS, New Delhi. In 2000, 2006 and 2007 he had solo exhibitions in Bangalore. In 2004 he had a solo exhibition at the Coomarswamy Exhibition Hall in Mumbai. In 2005 he had solo exhibitions at Shridharani Gallery, New Delhi and at CIMA, Kolkata. In 2007 he had a solo show at Art Indus Gallery, Delhi.

He has participated in several group exhibitions:
In 2010 he participated in the 'National Printmaking Portfolio' at Marvel Art Gallery, Ahmedabad. In 2013 he participated in a group show, 'Still Life' at Gallery Art Motif, New Delhi.

He has received several awards:
In 1971 he received the Nehru Fellowship Award for Research Work on Tribal Art, Gujarat. He was awarded the JD Rockfellar 3rd Fund Fellowship, USA. In 1989 he was awarded the Padma Shri. In 1991 he was announced the Regent Professor for Davis School of Environment Design, University of California in USA.

He lives in Ahmedabad.