"People are very afraid," UNHCR head Antonio Guterres said in a statement.
Incumbent President Laurent Gbabgo has refused to hand power over to former Prime Minister Alassane Ouattara, who is widely recognized as the winner of presidential elections last year. The contest was meant to unite a country divided by civil war but instead led to escalated political violence.
The UNHCR said at least 35,000 Ivorians have fled the country to neighboring Liberia, which is still recovering from its own internal conflicts.
"We face the risk of a possible massive displacement of Ivorians," added Guterres.
Gbagbo reportedly banned broadcasts by the United Nations on Thursday, though a U.N. spokesman said the radio station run by the U.N. peacekeeping mission there was still on the air.
U.N. broadcasters said, however, that the media was "muzzled" by supporters of Gbagbo.
Several people were reportedly killed in the Ivory Coast this week as fighting continued. Financial records were destroyed Tuesday when the country's Treasury building caught fire.
A spokesman for the Economic Community of West African States said the region was worried the situation would escalate to civil war.