A statement said that Pope Francis had agreed with the decision but did not say whether it was the pope's idea that O'Brien should leave for what the Vatican said would be "several months for the purpose of spiritual renewal, prayer and penance".
The statement did not say where the Cardinal was going.
More top news
The Government scheme would benefit those aged under 40 but will only run for five years.
Joseph Rowntree Charitable Trust and the Roddick Foundation are under investigation by the watchdog over grants made to Cage.
The Duke of Cambridge became a fearsome samurai warlord - at least temporarily - when he visited the set of a long-running Japanese drama.