The ICRC, one of the last agencies working in rebel-held areas, said militants had stopped its lorries since the middle of last month in the Middle Shabelle and Galgadud regions.
“The suspension will continue until we receive assurances from the authorities controlling those areas that distributions can take place unimpeded and reach all those in need, as previously agreed,” Patrick Vial, head of the ICRC delegation for Somalia, said.
The ICRC said it was talking to al-Shabaab, an Islamist rebel group linked to al-Qaeda, to try to solve the problem.
The rebels, who are hostile to western intervention in the lawless African country, outlawed 16 relief agencies in November.
Somalia has been mired in anarchy since warlords toppled military dictator Mohamed Siad Barre in 1991.
Abdullahi Haji Hassan, Somalia’s agriculture minister, said the rebels’ action would cause another humanitarian crisis.
Some 250,000 Somalis already live in famine conditions and a total of four million need aid, according to UN figures.