The 30-year-old, a 12-time Grand Slam champion, is ranked 12th after returning from an elbow injury at the Australian Open in January.
Losing to the 175th-ranked Kokkinankis will cost Federer the world No. 1 ranking.
The world number 175 was not expected to pose much of a challenge for Federer on a glorious Saturday in Florida, but Kokkinakis showed no fear to fight back a claim a sensational 3-6 6-3 7-6 (7-4) victory.
Djokovic, who lost in the fourth round of the Australian Open and dropped his only match at Indian Wells last week, had not lost in three consecutive tournaments since the end of the 2007 season, when he dropped his final five matches.
Djokovic lacked the movement that has made him such a force and his stray backhand put the Frenchman a break up at 4-2 in the second set. Just it's impossible at the moment. "I wouldn't go out on the court if I didn't believe I can win a tennis match".
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"I like to see Argentinian fans around the courts, Latino-American people, also", Del Potro said. "Of course, Novak is not playing like he was playing before, but I hope he's going to be 100 percent soon". I'm aware of that.
On Friday, Del Potro plays the same first opponent he beat previous year, Robin Haase.
That match in Indian Wells, Djokovic's first since he underwent a "small medical intervention" on his problematic right elbow marked Djokovic's worst ATP Masters 1000 loss since 2008 when he lost in the second round on Key Biscayne.
The Serb reiterated prior to match that he is playing pain-free for the first time in "years", a bold statement which makes you wonder whether his pragmatic approach is just a way to shift the spotlight and take things slowly. I wanted to get a couple tournaments before the clay-court season starts. "The circumstances that I was in the last two years were very challenging".
"I'm trying, but it's not working". I obviously wasn't ready.
"I don't know what to expect", Djokovic admitted.