Djokovic became the first man to reach the French Open quarter-finals for 10 successive seasons.
Nishikori, who was reached the final in Barcelona three times, winning twice, failed to make it for a fourth time.
Nishikori will take on Russian Daniil Medvedev on Saturday after the seventh seed stopped lucky loser Nicolas Jarry of Chile 6-3, 6-4.
Fifth seed Nishikori reached the final here last year but will lose a chunk of ranking points after losing to Herbert.
Federer is due for a return to the dirt after two seasons completely off the surface in three weeks at Madrid
Nishikori lost to Poland's Hubert Hurkacz 7-5, 5-7, 6-2, who moved into his first ATP quarter-final.
Top seed Nishikori beat Benoit Paire 6-4, 6-3 and will now face Huburt Hurkacz in the second round.
Switzerland's 2015 champion needed almost two and a quarter hours to defeat the Japanese star who was playing at the Dutch event for the first time.
Djokovic was leading 6-1, 4-1 after 51 minutes before Nishikori retired.
Marathon man Nishikori has already spent 13hr 47min on court in Melbourne this year, more time than any other player, coming through three five-set epics in his four matches so far.
The 29-year-old Nishikori has won all three of his first week matches on the same Melbourne Park second showcourt to reach the last 16 of the Australian Open for the seventh time in nine appearances.
Serena Williams is bidding to match Margaret Court's record of 24 Grand Slam titles on her first return to Melbourne Park since winning in 2017 while eight weeks pregnant.
Anderson won the first 11 games and needed only 64 minutes to demolish the woeful Nishikori in a remarkably one-sided group stage clash at London's O2 Arena.
The result means Federer is now in danger of failing to qualify for the semi-finals for just the second time in 16 appearances at the event.
Nishikori faces qualifier Daniil Medvedev in Sunday's Tokyo final after the beanpole Russian overpowered Canada's Denis Shapovalov 6-3, 6-3.