The towering Argentine has been out for 10 months after undergoing surgery to fix a left wrist issue and went down 7-6(5) 7-6(3) to Kukushkin, ranked 66th in the world.
Defending champion Del Potro, who won the U.S. Open in 2009, has seen his ranking plummet to 338 and had hoped to get some match practice in Sydney before the Australian Open begins in Melbourne on Monday.
There was not much to choose between the two players, who went unbroken throughout the match, barring a few points in the tiebreakers.
"It was a tough match," said Del Potro, who beat top seed Fabio Fognini in his second match. "I think he deserved to win because he played better than me in the tie-break.
"I served well, but my wrist hurts a little bit more than yesterday, and I couldn't hit harder than my last match. I think anyway it's a great week for me.
"I played three matches in a row and I played against good players, which means a good comeback for me."
Two-time Wimbledon champion Petra Kvitova signalled her intent for Melbourne by brushing aside Bulgarian Tsvetana Pironkova 7-5 6-1 to set up an all-Czech final against Karolina Pliskova.
With her win, second-seeded Kvitova brought Pironkova's dream run at the Sydney Olympic Park to an end after she won 14 straight matches, having come through qualifiers to win in 2014 and again playing qualifiers to reach the main draw this year.
Pliskova accounted for German fifth seed and world number nine Angelique Kerber, who went down tamely 6-3 6-2 after coming through a series of three-set marathons, including one that finished later than 3 a.m.
Australian Casey Dellacqua's progress before her home open was also halted after the top seed bowed out of the Hobart International with a second-round loss to Italian Karin Knapp.
The world number 29, however, did not seem too worried by her 7-5 2-6 6-3 defeat.
"I feel ready for the Australian Open and I feel that I'm the best prepared that I can be and that I have done everything that I possibly can," Dellacqua, Australia's best hope at the year's first grand slam behind Samantha Stosur, told reporters.
"Now I just turn my focus onto the Australian Open and doing what I can in the next couple of days to prepare best for that."
(Writing by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
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