ICRC officials said a letter from the government of Sudan said the suspension was for "technical" reasons, CNN reported.
The group said it has been providing humanitarian aid in Sudan for 36 years.
"We help people affected by the conflict in Darfur, provide seed, tools, food and water, and re-establish contact between people separated by the fighting," the ICRC website says. "The ICRC also promotes international humanitarian law and the protection of civilians affected by the conflict."
Fighting between the government of President Omar al-Bashir and rebels in Darfur has killed thousands of people and turned many more into refugees.
Sudan has suspended and expelled other aid organizations from Darfur.