Abidjan is the country's commercial capital, but residents were hurrying to find transport out of the city amid fears of an all-out civil war, the U.N. report said.
The report said up to 30 unarmed civilians were killed and 60 others were wounded when a market in a northern suburb was attacked with mortars.
The bombardment was carried out by members of the Ivorian military. Those forces are loyal to former President Laurent Gbagbo, who lost a U.N. certified election in November to opposition leader Alassane Ouattara. Gbagbo has refused to step down.
The suburb where the attack took place, Abobo, is considered a Ouattara stronghold, the U.N. report said.
Some of those fleeing the city did so after an appeal Saturday by pro-Gbagbo youth leader Charles Ble Goude, who called for civilians to join the ranks of the armed forces.
The U.N. report said thousands of youths have responded.