The 46th-ranked Seppi conquered Federer for the first time in 11 meetings, 6-4, 7-6 (7/5), 4-6, 7-6 (7/5) in almost three hours on Rod Laver Arena.
The Italian was to face either Australian Nick Kyrgios or Tunisia's Malek Jaziri in the fourth round.
It was a stunning win for Seppi, who had only taken one set off the 17-time Grand Slam champion in their previous 10 encounters.
It was Federer's earliest exit from the Australian Open since 2001, while he was knocked out in the second round at Wimbledon in 2013.
Federer was chasing his fifth Australian Open crown, but has now not won a major title since Wimbledon in 2012.
Composed Seppi kept the Swiss star under pressure throughout the match and broke him three times, winning with a magnificent passing backhand with Federer stranded at the net.
Seppi hit 50 winners, while Federer made a total of 55 errors.
"I just tried to enjoy playing on centre court again, it's not often that I get a chance to play on centre court," Seppi said.
"I just tried to do my best and it was one of my best matches for sure to win against Roger.
"Even with a two sets lead you never feel comfortable against Roger Federer, but I was focused on my service games and I didn't have many chances on his serve.
"It was a great tiebreak, especially with the last points."
Federer insisted there was nothing to take out of his early departure after reaching the semifinal stage for 11 consecutive years in Melbourne.
"To me I don't read anything into that (the loss)," he said.
"It's just not the best feeling to have," the 33-year-old Basel native said.
"It's not like I'm playing shocking or I'm feeling shocking. If I were you, I wouldn't read very much into that."
Seppi had the Swiss great off balance at Rod Laver Arena, where the big stadium crowd was fully behind Federer, urging him to fight his way back.
"I guess it was just an overall feeling I had today out on the court that I couldn't really get the whole game flowing," Federer admitted.
"It's just when it counted the most somehow it just ended up going his way," he said.
"I think that was because overall I wasn't feeling it quite as well," Federer added.
"I had to play it a little bit passively at times when normally I would play aggressive, it was just a tough match for me."