The General Authority of Civil Aviation (GACA) confirmed the death and said the injured were taken to hospitals for treatment. The strike hit terminals 3 and 4, which serve domestic flights, according to the authority.
The attack came a day after a Houthi missile killed 12 people and wounded more than 300 at the same airport, in the deadliest strike on Saudi soil since the US-Israel war on Iran began in late February. India's embassy said one Indian citizen died on Sunday from injuries sustained in Saturday's attack, potentially raising Saturday's toll to 13.
A witness aboard a taxiing aircraft told Reuters that a projectile struck the tarmac near parked planes at about 8:30pm local time, causing a fire. The aircraft returned to the gate and passengers were told to leave.
Houthi rebels claimed responsibility for the strikes prior to Sunday's attack. The Saudi-led coalition, which backs Yemen's internationally recognised government, has been fighting the Iran-backed Houthis for years.
The assault on the capital's airport has raised fears of wider regional conflict. US President Donald Trump has said he is weighing whether to join the fight against the Houthis, but no decision has been announced. The escalation threatens global oil supplies and shipping through the Bab al-Mandeb strait, a crucial waterway that Houthi forces have seized key areas along in recent weeks.