A search operation was under way to find two charity workers still missing.
The head of the ICRC called the incident the "worst attack against us" in 20 years, but the group said it did not know who was responsible.
Taliban spokesman Zabiullah Mujahid told Al Jazeera his group was not involved in the attack.
The governor of Jowzjan province, Lotfullah Azizi, said the aid convoy was attacked by suspected Daesh (ISIL) gunmen.
A massive snowstorm dumped as much as two meters of snow on areas of Afghanistan over the weekend, causing an avalanche that killed more than 100 people.