Svitolina received medical treatment after the second game and then retired when trailing 3-0.
The Ukrainian No.19 seed broke down in tears as she walked off Margaret Court Arena.
Svitolina took a year-long break from the tour for the birth of her daughter Skai in 2022 and had reached at least the round of 16 in three of the four majors since her return.
Elina Svitolina received medical assistance before her withdrawal. (Lukas Coch/AAP PHOTOS)
Noskova, who beat world No.1 Iga Swiatek from Poland in a huge upset in the third round, said she felt for her opponent.
"Obviously today was not the way I had planned to win," said Noskova.
"I feel sorry for Elina, I hope she gets very well soon."
Noskova's quarter-final opponent will another unseeded player, Ukrainian qualifier Dayana Yastremska, who downed former world No.1 Victoria Azarenka 7-6 (8-6) 6-4.
Dayana Yastremska is a shock Australian Open quarter-finalist. (Joel Carrett/AAP PHOTOS)
"It feels like my heart is going to jump out of my body," said an emotional Yastremska, who won six of the last seven games and hit 37 winners in the see-sawing encounter.
"I was losing the tiebreak, I was losing the second set, I always felt like I was running behind the train.
"But I think I'm a little bit of a fighter so that's why I won this match."
Azarenka was unable to convert either of her two set-point opportunities in the opening set.
The Belarusian won the 2012 and 2013 Australian Open crowns.
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