The first set was a tight affair which went with serve until Tsonga took his first break opportunity to secure the first set 7-5.
Murray, who had not played since the Davis Cup World Group play-off win over Croatia in September, immediately broke the Frenchman but went down 6-3 after Tsonga secured two breaks of his own.
"The courts here are very fast and you have to react quickly," said Murray.
"Jo was sharper than me, he served very well."
Murray, who was crowned BBC Sports Personality of the Year after winning Wimbledon in the summer, had missed the French Open with the back problem and was also absent from the season-ending World Tour Finals.