The illustrious physicist Dr. Vikram A. Sarabhai (1919-1971) was the honorary, part-time director of the Indian Institute of Management Ahmedabad during the initial years of the Institute. He was born on August 12, 1919 in a family of industrialists. He completed his Natural Sciences Tripos at St. John's College, Cambridge in 1940. He received his Ph.D. in 1947 from the University of Cambridge. On his return to India, he founded the Physical Research Laboratory (PRL) and the Ahmedabad Textile Industry Research Association (ATIRA) in 1947. The latter body engaged in research activities on management issues often collaborating with international experts.

When the Government of India announced the setting up of a national institute of management education in the 1950s, the Ford Foundation's India Office under the stewardship of Douglas Ensminger supported the engagement of consultants from the United States to help in the planning. In 1959, George Robbins of the University of California, Los Angeles, recommended the establishment of a management education institute. Mumbai, then Bombay, was the first choice location but the newly formed state of Maharashtra was a little slow to respond on the proposal and Sarabhai lobbied strongly for the new institute to be set up in Ahmedabad. He persuaded local industrial houses, led by the redoubtable Kasturbhai Lalbhai, to pledge their support for building the Institute's infrastructure, and convinced Dr. Jivraj Mehta, the first chief minister of Gujarat to allot land for the Institute. Dr. Sarabhai, Shri Lalbhai and Dr. Mehta played key roles in setting up the Institute. In March 1961, Sarabhai finalized a draft Memorandum of Association that visualized an equal partnership between the government and local industry. This draft was, however, modified by the Government of India in favour of a stronger role for the central government. Finally, after much negotiation, IIMA came into being on December 11, 1961, as a partnership among the Government of India, Government of Gujarat and Ahmedabad's industry represented by the IIMA Society. Dr. Sarabhai was appointed as part-time director in June 1962; a full-time director, a retired civil servant, was indeed appointed in 1963, but he could not join due to certain administrative reasons. Dr. Sarabhai continued as honorary director till Prof. Ravi Matthai, took over as the first full-time Director in August 1965.

Dr. Sarabhai's tenure oversaw the initial recruitment of faculty members, and the development of the Institute's initial management development programs and the long-duration postgraduate programme. IIMA launched its highly rated 3-Tier Management Development Programme in 1963-64, and its two-year Postgraduate Programme in Business Administration (PGP) in 1964. Though the Institute started by offering a postgraduate diploma in business administration, its concern for a broader role for 'management' in addressing national needs became evident in the establishment of the AGCO (Agriculture and Cooperatives) Group in 1963.

Dr. Sarabhai was instrumental in establishing partnerships with two of the Institute's key stakeholders. The Ford Foundation contributed resources for enlisting the help of the second stakeholder - the Harvard Business School, the library and later for some of the buildings. The Harvard Business School provided mentoring support for the first few years of the Institute's life by sending some of its faculty members regularly to Ahmedabad and also training about 25 faculty members of IIMA through its one-year International Teachers' Programme. The Buildings Committee was set up and Louis Kahn was invited to design the architecture of the campus. Dr. Sarabhai played a key role in the development of the IIMA logo by choosing an exquisitely carved sandstone lattice window of the sixteenth century Sidi Saiyyed mosque in Ahmedabad as symbolic of the Institute's search for excellence. He was appointed as Chairman of the Atomic Energy Commission of India and is considered to be the father of India's space programme. He was awarded the Padma Bhushan in 1966, and the Padma Vibhushan, posthumously, in 1972. He died on December 30, 1971. In early 1972, the Institute named the IIMA Library after Vikram Sarabhai. In February 1976, a bronze bust of Dr. Sarabhai was installed in the library.

Vikram Sarabhai's wife, Mrinalini Sarabhai (1918-2016), was an eminent Indian classical dancer and founded the Darpana Academy of Performing Arts in 1949, another hallmark institution of Ahmedabad attributed to the Sarabhai family.