In a statement carried by al-Masirah television network, the Yemeni Interior Ministry announced that Zaid was shot while driving with his daughter in the Yemeni capital, Sana'a, on Tuesday.
The assassination operation claimed the minister’s life and injured his daughter, it added.
The targeted killing of Zaid is a criminal act, which is part of the aggressors' schemes to remove Yemeni national figures, the ministry said, noting that an investigation was underway to bring criminals to justice.
Saudi-owned Al Arabiya TV channel described Zaid as an important leader of Yemen’s Houthi Ansaruallh movement.
So far, no group has claimed the responsibility for the attack.
Saudi Arabia launched a devastating military aggression against its southern neighbor in March 2015 in collaboration with a number of its allied states, and with arms support from the US and several Western countries.
The aim was to return to power a Riyadh-backed former regime and defeat the Houthi movement that has taken control of state matters since the resignation of the then president and his government.
The war, however, has failed to achieve its goals, but killed tens of thousands of innocent Yemenis and destroyed the impoverished country’s infrastructure. The UN refers to the situation in Yemen as the world's worst humanitarian crisis.