The Swiss, who would be chasing a record 17th grand slam title in Australia, was confident however that he would be fit for the tournament in Melbourne, which starts on January 16.
"I hurt my back in the second round match (on Wednesday)," Federer, who won the last of his 16 grand slam titles in Australia two years ago, told a news conference.
"I don't think it's the right time to risk anything right now. For Australia, I'm optimistic. It's not good, but it isn't crazy bad.
"Without playing and the right treatment I will get through it in the next few days. I have a long journey to Australia, but hopefully mid next week I should be 100 percent again," added the world number three.
Federer started the Qatar tournament in imperious form, dropping just nine games in his opening two matches, but he struggled in Thursday's quarter-final against Andreas Seppi, edging through 6-3 5-7 6-4.
He revealed his hurt back early in his second round clash with Slovenia's Grega Zemlja.
"Then I wasn't able to serve properly anymore. I had the same thing yesterday," said Federer, 30.
"I was really playing, you know, with the hand brake on, and I was just trying to manage the situation, really.
"(When) you're trying to protect the back, you might tweak something else. It's very dangerous.
"I've already played two matches in pain now, and it just gets a bit too much for the body."
The injury is muscular, with the Swiss using massage and stretches to treat his troubled back, as well as hot baths.
"It's helped a little bit but not enough to win this tournament, that's for sure," said Federer, who was the second seed in Qatar.
"You can just get through it sometimes if you have a couple of days off here or a day where you can work a lot with painkillers. But I don't have any days off.
"I warmed up this afternoon and was feeling okay, but serving and running was difficult."
Federer had been due to play Frenchman Jo-Wilfried Tsonga in the semi-finals on Friday. Tsonga will now meet either top seed Rafael Nadal or compatriot Gael Monfils in the final.
"It's really sad," Tsonga told a news conference. "It was good for me to play against him (Federer), to see how my level is and (how) I feel at the beginning of the season.
"I don't know if it's an advantage or a disadvantage (to now have a rest day), because I want to play. I need some time on the court to feel better for next week."
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