In 2005, the competition was ridiculed for awarding the prize to Christina Mackie for a sculptural installation of a papier m‚ché egg topped with a crystal ball.
A spokeswoman for the Institute said today it would be collaborating with Beck's this year on a music-arts project to commemorate the gallery's 60th anniversary.
She added: "There is no information on this right now - we will be making an announcement shortly."
Evening Standard art critic Brian Sewell welcomed the end of the prize: "I'm glad to hear of this. It's been one of the most wretched prizes in arts sponsorship history. Beck's Futures has been a going-nowhere exercise that hasn't done Beck's any good.
"The ICA is a tart who will let anyone f**k them for the right amount of money."