A statement says Abdulhafid Yusuf Ibrahim, a Somali national, died Wednesday night of his injuries after the attack in Mogadishu.
Somali police said two others were wounded after the bomb attached to their vehicle exploded near the ICRC office.
The Somalia-based extremist group al-Shabab, which is linked to al-Qaida, claimed responsibility. The group often targets high-profile areas of the capital.
The ICRC said it was “shocked and deeply troubled” by the attack and that another staffer was recovering with minor injuries.