World No. 36 Kyrgios was given a code violation for unsportsmanlike conduct after being broken early in the third set.
Having already been handed a code violation earlier in the match, the latest outburst meant the umpire also handed him a game penalty.
This prompted an angry Kyrgios to slam his racket into the ground and kick a water bottle before he tossed a chair toward the centre of the court.
The frustrated Kyrgios, 24, shook hands with his opponent and the umpire before he strode off the court, effectively defaulting himself from the contest.
The Australian's outburst comes just a day after he launched an astonishing attack on some of the biggest names in tennis as part of a podcast at the Rome event.
Ruud was leading 6-3, 6-7 (5), 2-1 when Kyrgios was disqualified and will face Juan Martin del Potro in the third round.