Melamede was born in New York City, while her mother, Israel Prize-winning architect Ada Karmi-Melamede, was a lecturer in the Department of Architecture at Columbia University. Her maternal uncle, the architect Ram Karmi, and her grandfather, the architect Dov Karmi.

Following her sister and brother's enlistment in the army, her parents returned to Israel. Melamede decided to stay in the United States and enrolled in architecture studies at Yale University. In 1997, after working with her mother for a year and a half, she decided to abandon architecture and pursue filmmaking. She returned to New York City and studied film in an intensive six-week course at New York University. She began working as an intern, then as an assistant.