"As long as the teams participating in UEFA competition have enough eligible players and the public authorities in each country have not imposed any contrary restrictions, all the matches must be played on the dates laid down by the competition regulations," said European football's governing body in a statement on Friday.
Ukraine on Friday closed schools, banned all public events and imposed restrictions on people's movements around the country for a three-week period after confirming its first death from H1N1 flu.
World football's governing body FIFA said it was monitoring the situation ahead of next month's World Cup play-off between Ukraine and Greece.
Ukraine's national side are due to host Greece on November 18 in the second leg of their World Cup qualifying European playoff.
"FIFA closely monitors the development of the situation in the country," said a FIFA statement.
Last week's French league match between Paris St Germain and Olympique Marseille was postponed by the French federation after three PSG players went down with the illness.
The Mexican federation pulled their clubs out of the competition - the region's equivalent of the Champions League - in protest.
