The peacekeepers were monitoring the border security zone set up in 2000 at the end of a brutal two-year war which killed tens of thousands of people.
They have left after the Eritrean government cut off their fuel supplies.
Last week, the UN warned the two sides could return to war, as troops were being amassed in the security zone.
“Clearly the signs point towards a resumption of the conflict,” UN spokesman Yves Sorokobi told the BBC last week.
The BBC’s Elizabeth Blunt in Ethiopia says although the move is being described as temporary, it looks unlikely Unmee troops will be going back.
Our correspondent says that diplomats in Addis Ababa say privately they cannot imagine a return for Unmee and that this is the beginning of the end of the peace force.
Eritrea is angered at its neighbour’s failure to hand over Badme, the disputed town which sparked the conflict, which a Boundary Commission set up after the war, awarded to Eritrea.
Dec 2000: Peace agreement
Apr 2002: Border ruling
Mar 2003: Ethiopian complaint over Badme rejected
Oct 2005: Eritrea restricts peacekeepers’ activities
Nov 2005: UN sanctions threat if no compliance with 2000 deal
Dec 2007: Deadline to demarcate the border expires without agreement
Dec 2007: Eritrea cuts fuel supplies to the UN
Feb 2008: UN warns of a return to war as it withdraws from Eritrea
Eritrea accepted international surveillance of a large swathe of its territory as part of the peace agreement that followed the war with Ethiopia.
But with the Boundary Commission decision in its favour, Eritrea wants the international community to put pressure on Ethiopia to withdraw from Badme.
Having lost patience with the UN, it has managed to force out the 1,400 troops and 200 military observers by cutting off fuel supplies.
The government in Addis Ababa warned the UN against allowing itself to be humiliated by one party to the agreement, but has said it will co-operate in allowing the withdrawing troops to relocate to northern Ethiopia.
Our correspondent says the main practical issue now is whether the UN force will be allowed to bring all its vehicles and equipment out with it.
In a briefing to diplomats, many of whose countries have contributed to the mission, Unmee said it was determined not to leave anything of military value behind.
But the spokesman for UN Secretary-General Ban Ki-moon said that although some convoys had been allowed to cross into Ethiopia, others had been turned back by the Eritrean authorities.