Infantino said it was "likely (the stadia) would not be ready for June this year" as planned in the schedule for the event to be jointly hosted by the Ukraine and Poland.
But he said that this would not hamper preparations for the tournament.
"They will be ready by October at the latest, there will be sufficient time to test them from the month of October," said Infantino.
"We knew that it wasn't going to be easy. But in the end it will be a magnificent celebration of European football."
He added that UEFA have received most the necessary paperwork from the Ukrainian football federation, following accusations of alleged government interference which lead to UEFA threatening to withdraw the championships.
"The deadline of the end of the month (March) will be respected, the signs are encouraging," added Infantino.