Leavy suffered the injury during Leinster's 21-18 Champions Cup quarter-final victory over Ulster on Saturday after coming off the bench in the second half.
"Leinster Rugby can confirm that Dan Leavy had an initial scan yesterday on a complex knee ligament injury but needs further assessment this week," the club said in a statement.
"He has been ruled out for the remainder of the season and into next season to include the Rugby World Cup."
Leavy, 24, won the last of his 11 caps against Argentina in November after missing last year's Six Nations with a calf injury.
Ireland coach Joe Schmidt was already sweating over the fitness of flanker Josh van der Flier, who is out for the remainder of the season after undergoing groin surgery, but could return for the World Cup.
The Rugby World Cup kicks off on September 20 with Japan and Russia kicking off proceedings in Tokyo.