Ahmed was born and raised in Hyderabad, India, where his father served as a public servant and his mother as an active volunteer. While living in Hyderabad, Ahmed received his BSc in chemistry from Osmania University in 1968. With strong English skills from his school in India, Ahmed moved in 1970 to Pocatello, Idaho to attend Idaho State University, where he received another B.S. in 1972 and an M.S. in 1974, both of which were in microbiology. He then attended McGill University, originally with the goal of receiving a doctorate in microbiology, but, after questioning his motivation for the field, he dropped out of McGill and later worked as a research assistant there for two years. In 1981, he received his Ph.D. in microbiology from Harvard University after studying for four years in Bernard Fields's lab. Later that year, he left Harvard for the Scripps Institute to begin his postdoc.
