The Irishman, who turns 21 on Saturday, will remain at Craven Cottage until the summer of 2018.
Kavanagh, who can also play at left-back, has made a total of 11 appearances since his debut for the west London club last August.
He scored his first goal for the Whites in the 1-0 win at home to Norwich City in October.
Fulham midfielder Sean Kavanagh has signed a new contract with the Championship club.