After overcoming Danish qualifier August Holmgren first up, world No.85 Thompson suffered a 6-3 7-6 (7-4) second-round defeat to Ugo Humbert on Friday.
Just one break of serve, in the fourth game, was enough for the first set to go the way of the 21st-seeded Frenchman.
Both men were broken early in the second set, but then held firm until a tiebreak settled the contest.
The result leaves seventh seed Alex de Minaur and Chris O'Connell as the only Aussies left in the draw, after Adam Walton and Tristan Schoolkate were eliminated on Wednesday.
Sixth-seeded Ben Shelton, who hadn't played since suffering a left shoulder injury at the US Open, was beaten 6-2 6-4 by David Goffin.
Earlier in the week, Shelton said that despite the five-week layoff, he still hoped to qualify for the ATP Finals in Italy beginning on November 9.
Shelton is currently sixth in the points race for Turin, with eight making the finals, but his loss will put a dent in those ambitions.
"It's the first time that I've put myself in a good position, at this point in the year, to make Turin," Shelton told the ATP Tour website this week ahead of his match against Belgian veteran Goffin.
"Hopefully I get a couple more good results and get over the line."
Shelton's fellow American Frances Tiafoe, the 25th seed, also tasted defeat, going down 7-6 (11-9) 2-6 1-6 to Germany's Yannick Hanfmann.
Denmark's 10th seed Holger Rune progressed in straight sets, as did 19th-seeded Argentine Francisco Cerundolo and 31st seed Gabriel Diallo of Canada.
World No.4 Novak Djokovic won his second-round clash on Friday night.
The 38-year-old Serb won the battle of the veterans, beating 37-year-old Croatian Marin Cilic 7-6 (7-2) 6-4.
The top-seeded players in Shanghai all received first-round byes.
With AAP.
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