Former world number ones Lleyton Hewitt and Marat Safin also bowed out, the former losing 7-6 4-6 6-2 to Serb Janko Tipsarevic and Russian Safin going down 6-3 4-6 6-0 to Frenchman Nicolas Mahut.
Briton Andy Murray, the last man to beat Federer, reached the third round, however, along with Australian Open runner-up Fernando Gonzalez and eighth seed Ivan Ljubicic.
Federer, seeking his fourth Indian Wells Masters Series title in a row, received treatment for blisters at the end of the first set and looked sluggish throughout as his 41-match winning streak was ended by the world number 60.
The Swiss ten-times grand slam champion, whose last defeat was inflicted by Murray in Cincinnati in August, was hoping to break the professional era record of 46 successive wins set by Argentine Guillermo Vilas.
Federer said the pressure of closing on another record had not contributed to his defeat.
"It's no pressure at all because I take it match by match," Federer told reporters. "I'm concerned about winning my first round match against a lucky loser.
"It just shows you how tough it is. Today was just a grind for me from the start. First-round match is always difficult, but I've had an incredible run, not losing in the first round for over two years. So I'm really happy about that. Sooner or later it had to happen, so it's OK."
Federer celebrated his 161st consecutive week as world number one last month, breaking the 30-year-old record of American Jimmy Connors.
"It's great to beat the number one, I feel perfect," the 29-year-old Canas told reporters. "I dream about this, but I didn't expect it. I have confidence in my game but I know it's gonna be tough."
Canas outplayed Federer from the baseline, never allowing the top seed to control the centre of the court and sealing victory with a powerful inside out forehand.
Canas, who achieved his career-high ranking of eighth in 2005, returned to the tour last September after serving a 15-month suspension for a doping offence.
He lost in last round of qualifying for the tournament to German Alexander Waske, but earned a place in the draw when Belgium's Xavier Malisse withdrew due to injury.
Murray, seeded 13th, eased past South African Wesley Moodie 6-3 6-3 to reach the third round.
PASSING SHOTS
The 19-year-old Murray blunted Moodie's serve and volley attack by firing his returns low to the South African's feet and cleverly reading his opponent's passing shots.
The British number one, winner in San Jose this year, broke Moodie three times and was broken just once. He next faces Mahut who upset 23rd seed Safin.
"I returned pretty good today," Murray said. "High percentage of first serves, didn't make too many unforced errors, so it was a solid match."
Number 11 seed Tomas Berdych of the Czech Republic was not so lucky as he lost 7-6 6-4 to American journeyman Michael Russell.
Spanish seventh seed Tommy Robredo lost to Gilles Simon of France 6-7 6-3 6-0, and number 17 Marcos Baghdatis of Cyprus went down 7-5 7-5 to Guillermo Garcia-Lopez of Spain.
Fifth seed Gonzalez of Chile and Nalbandian advanced to the third round with three-set victories over Canadian Frank Dancevic and German Philipp Kohlschreiber respectively. Ljubicic struggled past Colombian Alejandro Falla 6-7 6-4 6-4.
