The attack appeared to be deliberate as the pair had been travelling north of the capital Sanaa with two other colleagues in vehicles "clearly" marked with the Red Cross emblem, said the Geneva-based ICRC.
"Sadly, two of our staff were brutally killed on their way back from Saada to Sanaa," spokeswoman Rima Kamal said, referring to the northern stronghold of Shiite Huthi rebels who have been battling loyalists of the exiled president.
"One of our colleagues passed away on the spot while another sustained critical injuries and was transferred to an MSF (Doctors Without Borders) hospital... Where he passed away shortly after," she told AFP.
The two others were unharmed.
Also Read
The head of the ICRC delegation in Yemen, Antoine Grand, said identified the dead as a field officer and a driver.
"The ICRC condemns in the strongest possible terms what appears to have been the deliberate targeting of our staff," Grand said in a statement.
But ICRC spokeswoman in Geneva Sitara Jabeen said that "after this incident we have stopped all our movements in the country for the time being."
The ICRC said it was not immediately clear who carried out the attack, noting there had been a number of security incidents involving the organisation in recent months.
On August 25, the ICRC said it had suspended its operations in Yemen's second city Aden after gunmen robbed its main office while holding staff at gunpoint.
The ICRC says it provides vital humanitarian support to hundreds of thousands of people in need across war-ravaged Yemen.
On Wednesday, Saudi-led coalition air strikes hit Saada and the rebel-held port city of Hodeida, witnesses said.