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Haider-Mauer started well, winning the opening game, but then lost 10 games in a row.
He sought medical treatment for a lower back injury after the first set and then retired in the second.
"I have no idea when his problems started," Seppi said.
"I tried to focus on my game and did not notice that anything was wrong with him."
It's Seppi's fourth appearance in the quarter-finals at Umag in as many years.
He improved his record to 9-3, with his best results being the semi-finals in 2009 and 2010 — when he lost both times to Spain's Juan Carlos Ferrero.
Horacio Zeballos from Argentina also advanced after rallying to defeat eighth-seeded countryman Carlos Berlocq 3-6, 6-3, 6-2.
Berlocq, who had won all but one of the last nine matches, including his first career title two weeks ago in Bastad, started off well but made too many unforced errors in the second and third set.
After winning the second set, Zeballos was up in 3-0 in the third before Berlocq produced a rally of his own to reach break point for 3-3.
However, Zeballos saved it, and then cruised to victory.
Results from the fourth day of the Croatia Open on Thursday (x denotes seeding):
Second round:
Aljaz Bedene (SLO) bt Aleksandr Dolgopolov (UKR x4) 6-3, 6-1
Horacio Zeballos (ARG) bt Carlos Berlocq (ARG x8) 3-6, 6-3, 6-2
Andreas Seppi (ITA x2) bt Andreas Haider-Maurer (AUT) 6-1, 4-0 - retired
