Kiev and Western governments warned Moscow against any attempt to turn the operation into a military intervention by stealth in a region facing a humanitarian crisis after four months of warfare.
Ukrainian presidential aide Valery Chaly said: "This cargo will be reloaded on to other transport vehicles [at the border] by the Red Cross."
"We will not allow any escort by the emergencies ministry of Russia or by the military [on to Ukrainian territory]. Everything will be under the control of the Ukrainian side."
Russian media said the column of 280 trucks had left from near Moscow and it would take a couple of days to make the 620-mile journey to Ukraine's eastern regions, where rebel fighters seek union with Russia.
A Russian orthodox priest marched down the line of lorries, spraying them with holy water before they left.
Western countries believe Russian President Vladimir Putin, who has whipped up nationalist fervour in Russia through the state-controlled media since annexing Crimea in March, might be spurred to fresh action since separatists in their main redoubt of Donetsk are now encircled by Kiev Government forces.
The US, French and Australian governments voiced concern Russia could use the humanitarian deliveries to carry out a covert operation to help fighters who appear to be on the verge of defeat.