The sale had been opposed by Irish government ministers and heritage groups.
The foundation, a charitable trust that runs Russborough House in Ireland, is selling paintings to fund a €15m endowment required for the upkeep of Russborough House in Co Wicklow.
The consignment, thought to be worth up to £5.3 million, was to be sold at Christie's King Street's Old Master and British Paintings Evening Sale on July 9 and the auction house's Old Master and British Paintings Day Sale on July 10.
The foundation asked for a postponement of the sale until October, to give it time to consider other options, including a "generous proposal" from a group of Irish donors.
A Christie's spokesperson refused to comment on whether the auction house will seek recovery of its marketing costs, which include pre-action viewings in New York and Hong Kong. "We can't discuss the nature of client contracts," he told ATG.
He added: "[The Foundation] want until October to explore other options as their 'Plan A' and if they decide to consign them into sale [after this time], that is up to them."