The world number two suffered a back spasm during her final round-robin match against Li Na and was heavily beaten 6-2 6-1.
That result was enough to put both Li, who emulated Serena Williams in winning all three of her group matches, and Jelena Jankovic into the last four from the white group.
Jankovic will play red group winner Williams on Saturday while Li will take on fifth seed Petra Kvitova, who won a straight fight for the final spot against Angelique Kerber 6-7 (3/7) 6-2 6-3.
Azarenka admitted after her defeat by Jankovic on Wednesday that she was mentally fatigued and struggling for motivation but it was not desire that was the problem on Friday.
The Belarusian had clawed her way back from 0-3 to 2-3 when, serving at 0-40, she locked her back on landing and yelped in pain.
Azarenka said: "I served really hard and just really locked my back. I don't know what really happened. It was just bad movement and a big spasm. I had no flexibility."
She went off court for treatment but her movement was severely compromised and she appeared to be in a lot of discomfort, struggling to stand up at each change of ends.
From the moment of the injury she lost eight straight games, finally getting on the board in the second set in the sixth game to avoid losing it to love.
Given her very limited movement, it was something of a mystery why Azarenka decided to complete the match.
The Belarusian has a reputation for withdrawing having done so 25 times either before or during matches over the past eight seasons.
"There are a few reasons," said Azarenka when asked why she carried on. "There is a no-win situation, retiring and it being discussed.
"I don't have a tournament next week. The physio told me there is no real structure damage but you can't fix it that quickly.
"The most important thing is I just wanted to try to do my best for the fans who came and watched our match, and out of respect for my opponent."
Pushed on whether she had thought criticism might have come her way had she pulled out, Azarenka said: "There could be, there could not be. I don't know. It's not like it never happened before."
A season that began with the 24-year-old winning a second successive Australian Open campaign has rather ended with a whimper.
She also reached the US Open final, losing to Serena Williams, and that was the start of a run of five defeats in six matches to finish the year.
Injuries have also been a problem, most notably a fall during her first-round match at Wimbledon that forced her to withdraw from the tournament.
Reflecting on her year, Azarenka said: "I think overall, if you look at the results and the numbers, I had a pretty good year. I'm number two in the world. I had great results at the big tournaments and I had injuries.
"So it's that balance of good and unfortunate. It just needs to be looked through more. I think I can learn a lot from these little things to prevent maybe some of the injuries.
"Some things you cannot but for the next year I will be much better, I'm sure about it."
Li had gone out in the group stages on both her two previous appearances at the year-end championships, and she was happy she managed to keep her focus to ensure progress this time.
The Chinese player said: "Today the match was not about tennis or about fitness, it was only about mentality. Because I thought maybe after the first set she would give up but she still tried to continue to play.
"It was tough because I had to focus all the time because you never know what can happen on the court.
"If I was feeling very bad, for sure I would retire because maybe if I continue it could be worse for the injury. But everyone is different."
Next up for Li is 2011 champion Kvitova, who won yet another three-set match.
The Czech is the WTA Tour's queen of going the distance, and she recovered well from losing a first set to Kerber in which she had led 4-1.
Kvitova cracked 47 winners in the three sets to reach the semi-finals for the second time.
Jankovic headed into the semi-finals on a losing note after going down 6-4 6-4 to Sara Errani.
It was a dead rubber, with Errani having been eliminated on Thursday, but the Italian showed impressive spirit to post her first win in this year's competition.
The result meant Jankovic, Errani and Azarenka all ended up with one win but it is the Serbian who progresses courtesy of her superior sets record.
Errani still has a title to go for in Istanbul, with her and fellow Italian Roberta Vinci beginning their doubles campaign on Saturday.