It is believed a lone gunman opened fire on their vehicle as they travelled through the northern province of Amran.
Aid agencies have been trying to reach millions of people in Yemen, who lack basic supplies because of the conflict that has been raging there for months.
The killings come just over a week after gunmen raided the ICRC's offices in the southern port city of Aden.
They held staff at gunpoint and demanded money, vehicles and other equipment.
The attack, one of at least 10 recent security breaches the ICRC has faced in Aden, prompted the organisation to temporarily suspend its local aid operations.
An ICRC statement said the field officer and driver - both from Yemen - were travelling with two colleagues in a convoy between Saada province and the capital, Sanaa, when the gunman stopped their vehicle and shot them.
One of the workers died at the scene, while the other was rushed to a nearby hospital where he succumbed to his injuries. Their two colleagues were unharmed.
"The ICRC condemns in the strongest possible terms what appears to have been the deliberate targeting of our staff," said the head of the ICRC delegation in Yemen, Antoine Grand. "Our thoughts and sympathy are with the families and loved ones of our colleagues."
"It is premature for us at this point to determine the impact of this appalling incident on our operations in Yemen. At this time, we want to collect ourselves as a team and support each other in processing this incomprehensible act," Mr Grand added.
ICRC spokeswoman Sitara Jabeen had earlier told the BBC that the ICRC would halt all movement by its staff in Yemen as a precaution.
It is not yet clear who carried out the attack.
Saada is a stronghold of the Houthi rebel movement, whose conflict with forces loyal to exiled President Abdrabbuh Mansour Hadi has escalated since a Saudi-led coalition intervened militarily at the end of March.
The fighting has now reached 21 out of 22 provinces and some 4,500 people - including at least 2,112 civilians - have been killed, according to the UN.
More than 1.4 million people have also been displaced and 21 million - almost 80% of the population - are in need of some form of humanitarian aid.
Yemen's humanitarian catastrophe
Who is fighting whom?
Meeting the Houthis and their enemies
The International Committee of the Red Cross (ICRC) says two of its local workers have been shot dead in Yemen.