The Milan midfielder needed extended treatment to his left leg after an eighth-minute challenge from Alex Pearce, and was taken off the pitch on a stretcher leaving his fitness for the showpiece in the balance.
Italy were far from their most fluent at Craven Cottage and were lucky not to be behind as Shane Long and Anthony Pilkington both missed good chances for Ireland.
Cesare Prandelli's side raised their game in the second half, but Montolivo's injury could be the major talking point ahead of the finals.
Italy started the game well with plenty of energy and created their first chance within five minutes.
Claudio Marchisio was given too much room in midfield and it took a fine save from David Forde to keep the Juventus man's 25-yard strike out.
The impressive start was halted almost immediately, though, with Montolivo's departure - and Ireland seized the initiative.
Long, Pilkington and David Meyler all had excellent sights of goal before the break for Martin O'Neill's men, but Salvatore Sirigu was equal to all of them and pulled off a series of excellent saves.
Ireland started the second half as they finished the first, and Long should have done better after escaping his marker early on, but again Sirigu was there to deny him.
Ciro Immobile had the ball in the net five minutes before the hour but after the Torino striker had converted Giuseppe Rossi's cross he was flagged offside.
Marchisio brought the only save out of Forde in the second half with a low shot after good work from substitute Antonio Cassano, however he was unable to convert on a frustrating night for the 2006 World Cup winners that nearly got worse as substitute Stephen Quinn struck the crossbar in 80th minute.
Italy now face one more warm-up game, against Luxembourg in Verona, before they travel to Brazil for their first match against England on June 14.
