Interior Ministry spokesman Maj. Gen. Mansour al-Turki says the group was also behind a suicide bombing near the US consulate in Jiddah.
Both attacks took place in July during the final days of the Muslim holy month of Ramadan. The bombing outside the Prophet Muhammad's mosque in Medina killed four security officers.
Al-Turki said today that 32 of those arrested were Saudis, while the 14 others were from Egypt, Pakistan, Yemen, Afghanistan, Sudan and Jordan. He spoke to reporters in Riyadh.