The third qualifying round game will now be played in Kiev in central Ukraine on July 30, at the Olympic Stadium, UEFA said Wednesday.
Copenhagen had asked UEFA not to play in Dnipro's home city in the troubled east of the country.
''We are satisfied that UEFA has listened to us and understood the many arguments that spoke against holding the game in Dnipropetrovsk,'' said Anders Horsholt, the Danish club's managing director. ''We would like to stress that we have no problems with our opponent FC Dnipro. This is only a matter of safety and sense.''
The switch came days after UEFA declared Dnipropetrovsk among four Ukrainian cities judged safe to host Champions League or Europa League matches.
Dnipro had announced the rescheduling - playing next Wednesday, one day later than originally planned - earlier on its Twitter account.
''UEFA has forbidden the hosting of the Dnipro-Copenhagen match in Dnipropetrovsk,'' the club said.
Dnipro finished runner-up in the Ukraine league last season, earning entry to the Champions League qualifying rounds. It needs to beat two opponents to join champion Shakhtar Donetsk in the lucrative group stage.
Shakhtar has said it will play home games in the western city of Lviv because Donetsk is under the control of pro-Russian separatist rebels.
Dnipropetrovsk is a largely Russian-speaking city 210 kilometers (131 miles) from Donetsk and has seen comparatively little unrest.