0241 GMT April 24, 2019
The Serb, who currently holds three of the four Grand Slam titles, was beaten 6-4, 6-4 by the German world number 39, BBC Sport reported.
Djokovic broke his racquet in anger after Kohlschreiber – who had lost his past seven matches against the 31-year-old – took the first set.
The match between Djokovic and Kohlschreiber began on Monday but was delayed until Tuesday because of heavy rain.
Kohlschreiber won 72 percent of first-serve points and saved four of five break points as he closed out victory.
"To be honest, I don't enjoy losing, especially in a tournament like this, a tournament where I have had plenty of success in the past," Djokovic said.
"But it just happens, one of those days. You just have to deal with it, move on, turn the next page.
"Miami is the next tournament singles-wise for me. I'm not at my highest level, but slowly building, and hopefully I'll be able to peak in Miami."
Osaka, Halep out
Meanwhile, World number one Naomi Osaka's defense of her Indian Wells title was ended in round four by Belinda Bencic.
Japan's Osaka, who holds the U.S. Open and Australian Open titles, was beaten 6-3, 6-1 by the Swiss world number 23 in just over an hour.
World number two Simona Halep or Romania is also out, beaten 6-2, 3-6, 6-2 by Czech teenager Marketa Vondrousova.
It was a first win over a top-five player for the 19 year old, who is ranked 61st in the world.
Halep's defeat in California means 21-year-old Osaka, who claimed her first WTA title with victory at Indian Wells last year, will keep her number one ranking, despite losing to 22-year-old Bencic.
"I didn't play that well," Osaka said. "Honestly, at a time like this with that scoreline, I would usually feel very depressed and sad.
"But I feel pretty good right now because I tried my best and I don't really have any regrets.
"She was just playing so well. There wasn't anything that I could do in that situation."
Bencic had beaten four top-10 players on the way winning a title in Dubai last month.
"I'm very confident with my game right now. I'm hitting the ball well. So just things worked out for me," said Bencic.