The 32-year-old had been hoping to follow up his victory over American Tennys Sandgren, his first ATP Tour singles win since January, with another success which would take him through to the quarter-finals.
But despite taking the opening set, and putting up a late fight against the seventh seed, Murray eventually fell 4-6 6-2 6-4 in a contest which lasted two hours and 42 minutes.
A nervy start cost Murray when he was broken by De Minaur in only the third game.
However, the former world number one recovered well and managed to level things at 3-3 before breaking his opponent again in the 10th to clinch the set.
De Minaur then stepped up the pace in the second set and Murray was unable to match it.
The Australian made his presence felt with an early break and then added another in game seven, before serving out to love to take the contest into a decider.
Murray faced two more break points in the opening game but was able to keep his seventh-seeded opponent at bay this time, and the set stayed on serve until the ninth when De Minaur went 40-0 up on the Murray serve.
The Scot had no comeback this time and De Minaur punished a weak second serve to leave himself serving for the match.
That proved no easy feat for the Australian, who had to fend off three break points against a determined Murray, but De Minaur managed to make his second match point count against the three-time grand slam winner.
Murray is continuing his comeback from the hip resurfacing operation he had in January and will now turn his attention to next week's China Open, where his name will go into the draw alongside the likes of two-time French Open finalist Dominic Thiem and reigning ATP Finals champion Alexander Zverev.
And although the Scot is pleased with his performances in Zhuhai this week, he will not be raising expectations in Beijing.
"The level in Beijing is a little bit higher in terms of the quality of players, so I'm not playing Top-20, Top-30 tennis right now, I'm probably playing Top-70, Top-60, sort of level," Murray told a press conference. "So it's not going to be that easy for me to win matches there.
"However, I can still make a few improvements in the next couple of days. It's Thursday night so I'll get a chance to rest from this week the next couple of days and then hopefully get a couple of good days' practice there in Beijing and wait and see what happens with the draw.
"There's a lot of good players there and I could play a Top-10 player in the first round, and I wouldn't be expecting to win that match right now."
