When IIMA started its administrative office in June 1962, it was operating out of a rented bungalow in Shahibaug, Ahmedabad. In the same year, the Government of Gujarat purchased and transferred 65 acres of land worth over Rs. 25 lakhs to IIMA and the governing board began to scout for a world-class architect to build a campus that would match the vision it had set for itself. Ahmedabad, home to a stunning array of architectural masterpieces built over several centuries, had already attracted international attention in the 1950s when Le Corbusier, a pioneer of modernist architecture designed Sanskar Kendra. Vikram Sarabhai and Kasturbhai Lalbhai wanted something on that level of grandeur and were put in touch with Louis Kahn in 1962 through the National Institute of Design (NID) and B. V. Doshi, then a young architect. Doshi knew Kahn through teaching assignments at the University of Pennsylvania where Kahn was based, was Consultant Architect for the IIMA campus and years later designed the campus of IIM Bangalore in the 1970s and won architecture's biggest honour, the Pritzker Prize in 2018.

Louis Kahn (1901-1974) was born in a region now known as Estonia in Europe and emigrated to USA at a young age with his parents. His artistic talents were honed from a young age and he graduated with a degree in architecture from the University of Pennsylvania. He worked on several projects before joining the faculty at Yale University in 1947 and the University of Pennsylvania in 1957 where he taught until his death.

Louis Kahn's IIMA project began with his visit to India in November 1962 and he soon began to conceive the IIMA campus in his distinctive style of architecture comprising circles and arches, using red bricks that were locally available. The architects and engineers at NID were part of the project and the construction contract was awarded to Gannon Dunkerly & Co. Ltd. The ground-breaking ceremony was done on 9th September, 1964. The first buildings built were the faculty houses, followed by the dormitories or student hostels, the main academic complex and other buildings. A lake was planned between the faculty houses and rows of dormitories but this eventually did not materialize. The first batch of students in 1964-65 stayed in apartments of the Gujarat Housing Board and took classes in rooms at ATIRA but soon the locus of academic activities shifted to the red-brick campus by 1966. A more detailed account of campus development and its philosophy is available in this 1969 article, written by M. K. Subramaniam, then the administrative officer of IIMA, and this 1987 article in the Alumnus magazine. Kahn's work on IIMA is preserved at the Louis Kahn Archives at the University of Pennsylvania and a documentary on his life was made by his son, Nathaniel Kahn, in 2003.

Louis Kahn's majestic red-brick campus is an architectural masterpiece mesmerising generations of people associated with the IIMA community. As described by one Japanese architectural journal- "Geometry and structure burst free to a degree almost shocking when seen in photography." IIMA alumni have a strong attachment to the dormitories they lived in and the spaces they interacted in, all carefully designed by Louis Kahn. Anant Raje (1929-2009), architect, was closely associated with IIMA for several decades and worked on completing Louis Kahn's designs as well as providing designs for new structures. Later additions to the campus include the Ravi J. Matthai Auditorium and office complex that were inaugurated in 1997 and several other buildings. In recent years, sections of the red-brick campus have undergone conservation and renovation. A campus-wide wall made of bricks was also built. Between 2001 and 2009, a new campus was designed by HCP Design, Planning and Management Pvt. Ltd., connected to the old one through a subway pass that runs under a main road. The land for the new campus was acquired by IIMA much earlier. The new campus was in sync with Louis Kahn's broad philosophy of design but used a different material, exposed concrete, similar to the Salk Institute in California, USA, designed by Kahn. Louis Kahn lives in the institute's memory on a daily basis, especially through the three letters - LKP - Louis Kahn Plaza where major events including the convocations are held.