Murray, 29, is bidding for a second Wimbledon and third Grand Slam title, while his Czech rival Tomas Berdych was runner-up at Wimbledon in 2010.
In the other semi-final, seven-time champion Roger Federer will take on Canada's sixth seed Milos Raonic.
Federer is aiming to win his 18th Grand Slam title and first since beating Murray in the Wimbledon final in 2012.
Federer and Raonic open play on Centre Court at 13:00 BST with Murray and Berdych's match following.
Since reuniting with coach Ivan Lendl before the Aegon Championships, second seed Murray has won 10 straight matches, including the final at Queen's.
Some wise judges believe the Scot is playing the best tennis of his career, even better than when he won the Wimbledon title in 2013.
If Murray sees off Berdych he will reach his 11th Grand Slam final, beating the British record held by Fred Perry since 1936.
Murray leads 10th seed Berdych 8-6 in head-to-heads, including their last four matches. Berdych, who lost to Rafael Nadal in the 2010 final, has never won a major title.