However, the match between Dnipro Dnipropetrovsk and Tottenham Hotspur will go ahead in Ukraine as planned.
That tie is being played around 300 miles from Kiev and the London club said in a statement: "We have been advised that the police in Dnipropetrovsk have been briefed to expect British fans and the situation there is stable and under control".
UEFA confirmed there were no plans to move the match.
Club president Amadeo Salvo told reporters at Valencia airport on Wednesday that "common sense" had prevailed and the game with Dynamo would be moved to Nicosia with the same kickoff time of 1800 GMT.
"The players are having something to eat and in a few hours we are flying to Cyprus," Salvo said. "It was very difficult to play in Kiev.
"They guaranteed our security but the situation is very unpredictable and cannot be controlled and the best thing is to play at a neutral venue.
"We are satisfied. Common sense and the cordial relations between all involved have prevailed. The best thing, the most positive, is there is no change to the date of the match or the La Liga calendar."
The Ukrainian government has launched a crackdown on protesters who have been occupying central Kiev for almost three months since Yanukovich rejected a trade deal with the European Union and accepted a $15-billion Russian bailout.
Salvo apologised to any supporters of the Spanish club who had already made the trip to Ukraine.
(Reporting by Iain Rogers; Editing by Rex Gowar)
