Kyrgios needed lengthy treatment on his left leg after taking a nasty tumble behind the baseline while stretching to make a shot in the ninth game of the first set.
The world number 20 decided to keep playing, but he was clearly affected by the injury and, after Young won the first-set tie-break 7-3, Kyrgios trudged to the net to withdraw from the Wimbledon warm-up event.
The 22-year-old was expected to make a strong run at the All England Club, but the injury leaves his participation at the grass-court Grand Slam tournament in jeopardy.
Having battled hip and shoulder problems in recent months, Kyrgios last week declared he was finally close to full fitness, but now he faces an anxious wait to discover if he will be able to compete at Wimbledon, which gets underway on July 3.
Jo-Wilfried Tsonga got back on track after his French Open nightmare as the world number 10 eased to a 6-2, 6-2 win over Adrian Mannarino.
Tsonga's strong start to his grass-court campaign was the perfect way to erase the painful memory of an embarrassing first-round exit against unheralded Argentine Renzo Olivo on the clay at Roland Garros.
That was the first time Tsonga had lost in the opening round of a Grand Slam in 35 appearances, but there was no hangover as he brushed aside fellow Frenchman Mannarino in just 66 minutes.
"For me it was really important to have a victory. On clay it was difficult. I didn't play really well in Roland Garros," said Tsonga, who was runner-up at Queen's in 2011.
"I had the good sense to have a grass court at my house, so I just practice and prepare this grass season, which is a good surface for me.
"Hopefully I will be able to do something good. It's good to be back."
Fifth seed Tsonga, who has won titles in Lyon, Marseille and Rotterdam in 2017, will play Gilles Muller or Nikoloz Basilashvili in the second round.
Morale-boosting win for Berdych
Former Wimbledon finalist Tomas Berdych halted his slump with a 7-5, 6-3 victory over Belgium's Steve Darcis.
Berdych, the world number 14, crashed out in the French Open second round to continue a disappointing year in which he has gone without a trophy and reached only one final.
The Czech veteran takes on Britain's Kyle Edmund or Canadian qualifier Denis Shapovalov in the second round.
Grigor Dimitrov, the Bulgarian world number 11, cruised into the second round with a 6-3, 6-1 win against Ryan Harrison of the United States.
Dimitrov is the only player other than reigning champion Andy Murray to win the Queen's title in the last four years and he looks in the mood to push the world number one for the crown this year after crushing Harrison in 54 minutes.
The 26-year-old, who made the Australian Open semi-finals in January, faces French qualifier Julien Benneteau or British wild card James Ward in the last 16.