The former world number one was making his first competitive appearance since losing in the Wimbledon quarter-finals in July, and had stressed that he had no expectations ahead of facing the Australian after undergoing hip surgery in January.
However, despite losing 2-6 7-6 6-5, Murray impressed on the show court at the London event and will now place focus on his recovery ahead of Wimbledon.
Murray began the match in style with a forehand winner, and two breaks of serve were enough for the 31-year-old to take the opener, but dropping the first set sparked Kyrgios into life.
The world number 21 quickly recorded two breaks of serve and although they were cancelled out by Murray, Kyrgios controlled a tie-break and took it 7-4.
Kyrgios had the better of the third, too, with Murray fending off five of six break-point opportunities as well as two match points in the 10th game.
However, at 5-6 down and with a 30-15 lead, Murray dropped three points in a row to eventually lose out in an encounter which lasted two hours and 39 minutes.