Yes, Imam was a Seyyed from a religious family that are descendants of Prophet Mohammad, through the seventh Imam, (Imam Mousa Kazem).
Ruhollah Mousavi was born to Ayatollah Seyyed Mostafa Musavi and Hajieh Agha Khanum, also called Hajar, in the town of Khomein, about 300 kilometers south of the capital Tehran, Iran, possibly on May 17, 1900 or September 24, 1902