"We are very much aware that the situation right now is catastrophic," Valentina Ferrante, the group's country director for Yemen, told the Thomson Reuters Foundation.
"If a family does not have the necessary economic resources to feed the entire family then they will select who to feed.
"Sometimes you get up to a point where a mother is literally forced not to feed certain members of the family, most probably the youngest one."
Yemen, one of the poorest Arab countries, is locked in a war that pits Iran-aligned Houthi rebels against the government backed by Saudi Arabia, the United Arab Emirates and the West.
The conflict and ensuing economic collapse have left nearly 16 million people, 53 percent of the population, in urgent need of food aid and famine was a danger if immediate action was not taken, the United Nations said this month.
The warring parties on Thursday agreed to cease fighting for the Houthi-held port city of Hodeidah, which is the main entry point for both commercial imports and aid supplies.
Ferrante said the biggest in challenge in delivering humanitarian aid was not money but gaining safe access to conflict areas which were being hit by airstrikes.
"We need to pass the message that we are neutral, so we are not involved in politics, we just need to deliver high-quality humanitarian aid interventions," she said.
Aid groups hailed the deal in Sweden as a "landmark first step" towards ending the conflict.
"The agreement from Sweden is incredibly encouraging to all of us who seek an end to the war and suffering in Yemen," said Johan Mooij, Yemen country director for aid agency CARE.
He said 80 percent of Yemen's commercial and humanitarian aid arrives through Hodeidah port.
"Only an end to the war can bring lasting relief to Yemeni people," said Tamer Kirolos of charity Save the Children.
"Until then, the international community must continue to put pressure on all sides to urgently address the humanitarian crisis to avoid a full-blown famine."
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