Keshishian was born in Beirut to Cecile Keshishian (née Simonian), and Kevork Keshishian, a pediatrician. The family immigrated to the United States in 1969. They lived briefly in Brookline, Massachusetts, and then moved to Manchester, New Hampshire. Immersed in the Armenian community, the Keshishians often housed Armenian refugees, and Keshishian and his younger sister, Aleen Keshishian, grew up speaking English and Armenian. Both siblings acted as children and toured with the New Hampshire Children's Theatre, American Children's Theatre, and the "I Like the U.S. of A" national touring company.
Keshishian attended St. Paul's School and Harvard University, graduating with honors in 1986. His senior thesis was a pop-opera adaptation of Wuthering Heights. The production, which included music by Kate Bush and Madonna, received significant attention.
