The Serbian had been 1-0 up in the first set against the German on Monday when the match was interrupted by rain.
When play eventually resumed on Tuesday, the tournament's top seed found himself fighting to gain momentum as German Kohlschreiber broke to lead at 4-3 before taking the opening set.
Djokovic's serve was under pressure again at the start of the second set as Kohlschreiber, the world number 39, moved ahead at 2-0 and then 5-2.
Although Djokovic fought back with a break of his own, Kohlschreiber was not to be denied as he delivered on a first match point opportunity.
Kohlschreiber next plays Frenchman Gael Monfils for a place in the quarter-finals.
Number four seed Roger Federer had no trouble overcoming compatriot Stan Wawrinka, racing to a 6-3 6-4 victory in a little over an hour.
The former world number one needed just a single break of serve in each set to seal the win.
He will now face Britain's Kyle Edmund in the fourth round, after the number 22 seed ousted qualifier Radu Albot.
Edmund won 84% of his first-serve points as he triumphed 6-3 6-3, putting an end to his Moldovan opponent's nine-match winning streak.
Earlier, world number seven Kei Nishikori suffered an unexpected exit after Poland's Hubert Hurkacz fought back to win 4-6 6-4 6-3 in just over two hours in the opening match on Stadium 2.
There was also disappointment for 10th seed Marin Cilic as the Croatian lost 6-4 6-2 against Canada's Denis Shapovalov.
Second seed Rafael Nadal, though, had little trouble seeing off Diego Schwartzman in straight sets.
The world number two, who has won the Indian Wells title three times, delivered a 6-3 6-1 win in an hour and 17 minutes.
Nadal will next play qualifier Filip Krajinovic, who pulled off an unexpected 6-3 6-2 victory over Russian 14th seed Daniil Medvedev.
Number eight seed John Isner progressed as the American defeated Guido Pella of Argentina in straight sets, 6-3 6-4.
And Russia's Karen Khachanov dismissed countryman and lucky loser Andrey Rublev 7-5 6-3.
