Britain’s world number three and Olympic champion, who won his first Grand Slam at Flushing Meadows this year, was broken by the Serb midway through the first set and again at the start of the second as he lost in under an hour at the Zayed Sports City Tennis Complex.
The rain-affected match was the opening contest of the exhibition tournament in the Emirati capital, which is played on outdoor hard courts and usually boasts the top six available players on the men’s tour.
In the other first-round match on Thursday, world number five David Ferrer beat Tomas Berdych 6-2 6-4.
"I have some things to work on in the next few weeks, but I am looking forward to it," Murray said.
"I have been training very hard in Miami. I enjoy Australia and have had played some of my best tennis there, so I hope that I can do the same this year."
It was a lethargic performance from Murray, who somehow contrived to lose the opening set despite winning all-but four points on serve - all of which came in the same game as Tipsarevic broke to move ahead.
The Scot had chances to break back in both sets, but was unable to take two break points in the first and one in the second.
Tipsarevic, who suffered from illness at the end of the season and lost all his matches at the World Tour Finals in London, is looking to consolidate his place in the world's top 10, although this tournament does not offer any ranking points.
This year’s Abu Dhabi line-up includes 2009 winner Murray, defending champion and world number one Novak Djokovic, and Spanish number two Ferrer.
Czech star Berdych, world number nine Tipsarevic and Spanish number three Nicolas Almagro – a late entrant after compatriot Rafael Nadal withdrew through illness – make up the draw.