After receiving medical treatment on Monday when trailing 2-0, the No.19 seed only lasted one more game before pulling out.
She left Margaret Court Arena in a flood of tears.
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)
"I've had some injuries to my back before where it just was tiredness the next day of the match, but this one was really out of nowhere," said Svitolina.
"I felt like someone shot me in the back.
"But hopefully I will be back training in maybe one week.
"Of course, the long flight I had to Australia, that's not going to help.
"I will have to take one day at a time, have to do my recovery, do the scan as soon as I get back home, and go from there.
"Hopefully I don't have something serious."
Noskova, who beat Poland's world No.1 Iga Swiatek in a huge third round upset, said she felt for Svitolina.
"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 from Belarus 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."
As has regularly been the case at the 2024 Open when a Ukrainian has faced an opponent from Russia or Belarus, Yastremska refused to shake Azarenka's hand at the conclusion of the match.
Despite the ongoing Russian invasion of Ukraine, players from Russia and ally Belarus are allowed to compete on tour, but not officially under their countries' banners.
The 34-year-old Azarenka won the 2012 and 2013 Australian Open crowns.
