Murray was kept out of the French Open by the injury and was making his comeback in the second round of Queen’s against the man who knocked him out of the pre-Wimbledon warm-up tournament at the same stage last year.
The Scot, a two-times former champion at Queen’s and top seed, made an aggressive start to the match, clattering a running forehand into the body of Mahut up at the net on his way to setting up two break points.
The Frenchman saved them both, however, and Murray was forced to wait until the seventh game before finally making the breakthrough, sealing the lead with a cross-court forehand passing shot winner.
Murray served out the set with little trouble two games later before the rain started to wreak havoc on the match.
The players returned 52 minutes later only to manage a game and a half before again being forced off. A second return was only marginally more successful as two-and-a-half games were completed, all service holds, before the rain put a stop to the match for a third and final time.
Murray now faces the likelihood of having to play more than one match in a day if he is to repeat his feats of 2009 and 2011 when he lifted the trophy at the west London tournament.
Some matches were completed, however, with Leyton Hewitt reaching the last 16 with a 6-4 6-3 victory over Grigor Dimitrov.
The Australian, a four-time champion at the pre-Wimbledon warm-up event, marched into the last 16 at the expense of the Bulgarian world number 28.
The 32-year-old is well into the twilight of his career and a lowly 82 in the world rankings but broke his opponent, a decade younger, in the third game and went on to take the opening stanza.
Hewitt had not tasted victory since the first round of the Miami Masters in March before this week but the former Wimbledon champion was serving superbly, not facing a single break point, and broke in the opening game of the second set before wrapping up a 67 minute victory.
"I thought I played a really smart match," Hewitt said. "My first match here wasn't pretty, but I fought hard and got through it. That's what I needed to do. Then today it was a classy performance."
He will next face American 2010 champion Sam Querrey in the third round.
British wild card Dan Evans enjoyed a famous win over Finland's Jarkko Niemenen.
The world number 277 followed up his victory over world number 75 Guido Pella by beating the 13th seed 6-4 6-7 6-4.
Evans, who starred in Britain’s Davis Cup win over Russia in April, made an early break to win the opening set but was pegged back by the veteran - ranked 240 places higher - 8-6 in the second set tie-break.
But the 23-year-old, who recently won a Futures tournament in Sweden, hit back to make two crucial break in the decider and take victory in 108 minutes.
Second seed Tomas Berdych, playing his first match since a first-round defeat at the French Open, eased past Dutchman Thiemo de Bakker 6-1 6-4 in a match interrupted by rain.
Round 2 results:
2-Tomas Berdych (Czech Republic) beat Thiemo de Bakker (Netherlands) 6-1 6-4
5-Marin Cilic (Croatia) beat Ivan Dodig (Croatia) 6-3 6-4
7-Alexandr Dolgopolov (Ukraine) beat Santiago Giraldo (Colombia) 6-3 4-6 6-4
Lleyton Hewitt (Australia) beat 10-Grigor Dimitrov (Bulgaria) 6-4 6-3
Benjamin Becker (Germany) beat 12-Lukas Rosol (Czech Republic) 7-6(2) 7-5
Daniel Evans (Britain) beat 13-Jarkko Nieminen (Finland) 6-4 6-7(6) 6-4
16-Grega Zemlja (Slovenia) beat Sergiy Stakhovsky (Ukraine) 7-5 6-4
Kenny De Schepper (France) beat Rohan Bopanna (India) 6-4 6-3
Marinko Matosevic (Australia) beat Michael Llodra (France) WO