Murray, the world's No.4-ranked player, has been out of action since an operation in September to correct a long-standing back injury and was some way from his best as he went down 7-5, 6-3 in the first round of the Mubadala World Championship in Abu Dhabi.
Murray matched Tsonga for much of the first set, the contest going with serve to 6-5 before his opponent converted his first break-point chance with a precise lob to take the opener. Murray forced a break of the Tsonga serve in the opening game of the second set but was unable to maintain his advantage and breaks for Tsonga in successive Murray service games took him 4-1 ahead and the Frenchman served it out from there to wrap up a 72-minute victory.
The opening match of the invitational tournament ended with victory for David Ferrer, the world No.3, who defeated Switzerland's Stanislas Wawrinka 7-5, 6-1.
Ferrer progresses to an all-Spanish semi-final against world No.1 Rafael Nadal, while Tsonga will meet Novak Djokovic, the world No.2, in the last four. Murray will get more match practice under his belt when he meets Wawrinka in a fifth-place play-off.