Zaporizhzhia regional governor Oleksandr Starukh said Russian forces targeted the convoy heading to Russian-occupied territory.
He posted images of burned out vehicles and bodies lying in the road.
Russian officials did not immediately acknowledge the strike.
Mr Starukh said those in the convoy planned to travel into Russian-occupied territory to pick up their relatives and then take them to safety. He said rescuers were at the site of the attack.
Meanwhile, the UN Security Council has scheduled a vote on a resolution that would condemn Russia for its “illegal so-called referendums” in the four Ukrainian regions, and declare that they “have no validity”.
The US and Albanian-sponsored resolution would call on all countries not to recognise any alterations to the status of Ukraine’s Luhansk, Donetsk, Kherson and Zaporizhzhia areas.
It would reaffirm the UN commitment to Ukraine’s sovereignty, territorial integrity and independence within its internationally-recognised borders.
The Kremlin has announced plans to move on annexing Russian-controlled areas of the four regions on Friday, and Russia is certain to veto the resolution.
US ambassador Linda Thomas-Greenfield said earlier this week that if that happens, the US and Albania will put the resolution to a vote in the 193-member General Assembly, where there are no vetoes.
The draft resolution, obtained late on Thursday by The Associated Press, would order Russia to “desist and refrain from actions aimed at the partial or total disruption of the national unity and territorial integrity of Ukraine”.
It would also demand the withdrawal of all Russian troops from Ukraine.
Nato has also warned it would retaliate over any attacks on the critical infrastructure of its 30 member countries and joined other Western officials in citing sabotage as the likely cause of damage to two natural gas pipelines in the Baltic Sea.
The rising tensions around energy security in Europe come as Russia prepares to annex four regions of occupied Ukraine, a move widely condemned by the West.