Castaways on the long-running Radio 4 programme are asked which of their eight favourite tracks they would take to the mythical island.
But Young, 44, who had "been swotting for this interview like I was doing an exam", confessed she completely forgot to ask the question during the recording, which took place on location in Naypyidaw, Burma, following six months of negotiations.
The Scot said: "The experience was so intense and had such a surreal quality about it I forgot to ask her which of the eight tracks she would save."
Young said senior world affairs producer Nick Springate saved the day when he "frantically signalled to me by holding up a single finger".
She added: "My mind was busy doing cartwheels of joy."
Young travelled to Burma to interview the Nobel peace prize-winner for this Sunday's instalment of Desert Island Discs.
She said of her castaway: "Most of her choices are for family reasons – connections to her childhood, to her own children. She is a woman of humour, intellect and dignity - a showstopper."