Third-seeded Gilles Simon of France defeated compatriot Fabrice Santoro 7-6 (3), 6-1, and will next face Djokovic, who defeated Cilic 6-3, 6-4 in 1 hour 37 minutes.
Murray, ranked No. 4, was scheduled to play the final match of the day on Center Court against France's Richard Gasquet, who will now play fourth-seeded David Ferrer of Spain in the semis.
Ferrer, who beat Igor Andreev of Russia 7-5, 6-1, denied that Murray's withdrawal meant he would now have an easier semifinal.
"No, no. Murray going out doesn't make it any easier for me because Gasquet is a very good player,'' Ferrer said. "The last time I played against him, it was very tough.''
The Spaniard said his match against Andreev "was the best match I played here. I was very focused.''
Santoro, who reached the final of the inaugural tournament in 1993 and won in remarkable fashion in 2002, is playing his last year on the Tour.
"It has been something special,'' Santoro said. "When I first came here in 1993, Dubai was a brand new city and this was a brand new tournament, and I saw this place growing up since 17 years. So it's something special for me to leave the tournament today.''
The Djokovic-Cilic match was perhaps the best match of the tournament so far, with the Serb producing some superb returns to break Cilic three times and inflict only the second defeat of the year on the Croat. Cilic failed to convert any of his six break points.
"I was trying in the last three matches to find this exact rhythm, and that's what I finally did today,'' Djokovic said. "I think the key was movement and focus. I was really trying to move well in the point, be patient, and just wait for the chances, because I was returning very well.''
Murray's withdrawal was another blow for an event already hit by controversy and a spate of injury-related absences. Murray is a doubt for Britain's Davis Cup match against Ukraine next week after his doctor advised him to rest for a week to 10 days.
Earlier, World No. 1 Rafael Nadal and No. 2 Roger Federer withdrew with injuries, while defending champion Andy Roddick of the U.S., withdrew under protest. Russian world No. 5 Nikolay Davydenko and No. 9 Fernando Verdasco of Spain also opted out.
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