Murray, 32, will be playing his first match since an operation on a career-threatening hip injury in January.
British number one Kyle Edmund faces top seed Stefanos Tsitsipas in the Fever-Tree Championships singles draw.
In-form compatriot Dan Evans will play ex-world number three Stan Wawrinka.
British number two Cameron Norrie will take on last year's Wimbledon runner-up Kevin Anderson, while Jay Clarke is drawn against France's Lucas Pouille.
Murray would face brother Jamie and his new partner Neal Skupski in the semi-finals if both pairs win their opening two matches.
Skupski and Jamie Murray, who split from previous doubles partner Bruno Soares after the French Open, open up against French duo Nicolas Mahut and Edouard Roger-Vasselin.
Elsewhere in the singles draw, Argentine world number 12 Juan Martin del Potro opens up against 20-year-old Canadian Denis Shapovalov, while fast-rising teenager Felix Auger-Aliassime takes on former Wimbledon semi-finalist Grigor Dimitrov.
Andy Murray had his hip resurfaced in January and says he still has "quite a lot of work to do" before he can play in singles again.
He plans to play doubles in Eastbourne and then at Wimbledon if he has no problems at Queen's.
No player has ever resumed a singles career after a hip resurfacing operation, although American doubles player Bob Bryan returned five months after the surgery in 2018.
Murray's last match was a five-set defeat by Roberto Bautista Agut in the first round of the Australian Open.
Queen's begins on Monday.