Relief minister Rishad Badurdeen said the trucks will deliver the food to government district secretary offices in the Kilinochchi and Mullaitivu districts.
District secretary offices, as well as other government services including post and health services, and two state-run banks, have always operated in Tiger controlled areas despite the fighting.
Aid agencies have expressed fears that civilians trapped by the latest fighting could face food shortages.
However, the government has said there are enough stocks in the affected areas.
The food convoy went as army troops began fighting the Tigers on the outskirts of their Kilinochchi stronghold in the north.