The world number one and defending champion, 30, plays 24th seed Querrey on Centre Court at 13:00 BST.
Murray expects his return to be tested against the serving prowess of Querrey, 29, having beaten four unorthodox opponents on his way to the last eight.
Roger Federer, 35, plays Milos Raonic in the second match on Centre Court.
The Swiss seven-time champion, seeded third, lost to Canadian sixth seed Raonic in last year's semi-final but has looked in imperious form so far this year.
On Court One, Serbia's three-time winner Novak Djokovic plays Czech 11th seed Tomas Berdych, after Croatia's seventh seed Marin Cilic plays 16th seed Gilles Muller of Luxembourg, conqueror of world number two Rafael Nadal in round four.
After rain disrupted play on Tuesday, Wednesday's weather is forecast to be dry, overcast and cool, at about 21C.
'When he's dictating, he's very dangerous'
ublik, Dustin Brown, Fabio Fognini and Benoit Paire to reach the quarter-finals, Murray faces a much clearer task against the 6ft 6in Querrey.
The 29-year-old from California is second in the aces chart with 99 and a fastest serve of 137mph.
However, Murray has won more points at the net as he has been sent scurrying all over Centre Court in his first four matches, testing out the sore hip that disrupted his build-up.
"Like I said at the beginning of the tournament, I'll be able to get through seven matches if that's what I have to do," the Scot said after his win over Benoit Paire on Monday.
"Obviously I want to try to get to the final. I've done a good job so far here."
Murray has won seven of their eight previous matches for the loss of just two sets, but Querrey has played his best tennis at Wimbledon over the past two years.
The American upset then world number one Djokovic in the third round last year on his way to a first Grand Slam quarter-final, and has matched that feat 12 months on.
"He obviously likes the conditions here," said Murray. "He played really well last year.
"I maybe played one or two service games in the first set [against Paire] that weren't the best. Against Querrey, you can't really afford that. He's not an easy guy to break.
"When he's standing up on the baseline, hitting forehands, dictating, he's a very dangerous player."
Querrey knows what to expect from Murray, who has an excellent record against big servers and will play his 10th consecutive Wimbledon quarter-final.
"I haven't really learned anything [from previous matches]," said Querrey.
"He makes a ton of balls. He plays great defence. Who doesn't know that? I have to try to beat him playing my game."
Sam Querrey needed five sets to beat Kevin Anderson in round four
'I do believe good things can happen'
Yet to drop a set and with just two losses to his name in 2017, Federer is the favourite to reclaim the title he last won in 2012.
Twelve months ago, he lost to Raonic in a five-set semi-final that proved to be his final match of 2016, before he took an extended break to let his injured knee heal properly.
It worked better than anyone could have imagined as the 35-year-old returned at the start of the year to win his 18th major title in Australia, and is still riding that wave of confidence.
Raonic, 26, is not quite in the form of last year but remains a fearsome opponent on grass, with a fastest serve so far of 142mph.
"To beat a big server is a different kind of match," said Federer. "It's more of a penalty shootout.
"On the return I've got to keep going for it, keep staying aggressive. Positive attitude. I do believe good things can happen."
Federer is playing in a record 15th Wimbledon quarter-final
'I know what I need to do'
Djokovic, 30, returns to action for the second day in a row after his fourth-round match against Adrian Mannarino was delayed by rain, but the Serb won in three comfortable sets on Tuesday.
Berdych, 31, has impressed in reaching his first Grand Slam quarter-final for a year but is on the wrong end of a crushing 25-2 career record against Djokovic, having lost the last 12.
"For me, it's important to start off well," said Djokovic. "I've played him many times. I know what I need to do. Hopefully I can execute that."
The opening match on Court One will see a clash of two of the best grass-courters, with Muller hoping to build on his win over Nadal and Cilic through to a fourth straight Wimbledon quarter-final.
"I played Marin not too long ago at the Queen's Club in the semi-finals," said Muller, 34.
"I lost to him in three tough sets. Obviously he's playing good."