Flights from Reykjavik to the theme park capital of the world had been due to get under way on 30 September, supported by a connecting service from Stansted.
However, in a trading update, Play said higher fuel prices had forced it to rethink its fleet.
It will no longer lease the Airbus A321neo LR aircraft it needs to operate transatlantic and will instead lease an Airbus A320neo "at more favourable terms".
