In a statement issued on Wednesday, the International Committee of the Red Cross (ICRC) said that it was “deeply shocked and dismayed” by the death of Mr Saleh, who was expecting his fifth child with his wife.
“He was working as the adviser to the ICRC’s head of office in Aden,” the statement added.
Hussein Saleh, a 35-year-old Yemeni, was killed on Tuesday morning while undertaking humanitarian work in the north of Abyan province, it said.
Militants were also killed as Yemeni aircraft pounded targets in the region, but the number was unclear.
The US has been backing Yemeni forces in a battle to retake towns from the control of al-Qaeda-linked militants.
It deploys drones in the restive southern province of Abyan, where the army has recently recaptured several militant strongholds.
An ICRC representative in the capital, Sanaa, told the BBC that Mr Saleh had been working in a team of four when he was wounded in the strike, and later died of his injuries.
Dibeh Fakhr confirmed he was hit by an air strike, but could not say whether it had come from Yemeni forces or a drone attack, saying details were not yet clear.
Yemen’s military recently launched a campaign to retake of a string of towns and villages after a year of jihadist control.
Many militants are believed to have retreated to safe havens in the mountains where they enjoy tribal protection.