The 17-time Grand Slam champion Federer, who qualified with a perfect 3-0 round-robin record, was joined by Japanese debutant Kei Nishikori, who fought back from one set down to beat David Ferrer of Spain 4-6, 6-4, 6-1 on Thursday, reported news agency.
Federer, six-time champion of the season-ending tournament, demolished fifth seed Murray in 56 minutes to complete Group B play. It was the 250th indoor match win of his career.
"It wasn't what I was looking for when I went on the court. Everything he tried tonight came off. He has the ability to do that," said Murray. "I now have seven weeks before the next tournament. I have time to work on some stuff."
It was the joint worst tour-level loss of Murray's career. The Scot lost to Novak Djokovic 6-1, 6-0 in the 2007 Miami Open."I had the upper hand from the baseline, which hasn't always happened against him," said Federer.
"But I definitely was able to play on my terms. For me, things went very well. I was able to put Andy under pressure very often, and I think the match couldn't have gone any better for me really."
Nishikori, the fourth seed, recorded his 55th match win of a career-best season against Ferrer, who was a replacement for the injured Milos Raonic.
"It's never easy playing against David because he's very consistent from the baseline. If I want to win, I have to do something to break his tennis. From the second set, I was more aggressive. The final set was almost perfect," said Nishikori.
"Kei has improved his game a lot. He's a very great player. He has a very good future. I think he will be in the top 10 for a lot of years."Ferrer is competing at the season finale for the sixth time. He finishes his year with a 54-24 match record.