The Welsh team, who need a point to guarantee their progress into the last 32, were due to depart at 10am today, but fog grounded them at Cardiff Airport.
After finally getting the go-ahead, a problem with the aircraft meant that they were unable to take off until 5pm, which delayed their arrival until 8pm local time.
"We cannot control everything, especially the weather," PA quotes Swans coach Michael Laudrup as saying. "It is a very long day for the team. It started at 7.45am at the training ground in Swansea, first they had problems with the fog and then when the plane arrived it had mechanical problems.
"They will arrive about 9pm at the hotel, so when I heard that I cancelled training. If it's possible we will do some small things on Thursday just to get them moving.
"Of course, it's not ideal but let's not make it more dramatic than it is. The game is at 7pm so there will be whole day to prepare for it. We have to do the job."
Kuban Krasnodar take on Valencia hoping to pip Swansea to qualification from Group A.