The match was locked at 3-3 in the fifth set when officials called a halt.
And a thrilling encounter had to be halted after just under four hours due to Wimbledon’s strict 11pm curfew.
The decision drew a few boos from an enthralled crowd before a standing ovation for the players, who will now have to come back on Wednesday.
Kyrgios was playing only his third event of the year but did not look particularly rusty as he came from 3-1 down to take the first set, throwing in a trademark underarm serve for good measure.
But Frenchman Humbert, seeded 21 and in fine form on grass after his win in Halle hit back to lead 2-1.
Ever the showman, Kyrgios tried the tweener behind the legs shot when facing set point in the third, and as is so often the case, it let him down.
But a 43-second game of three aces and an unreturnable serve suggested Kyrgios meant business in the fourth.
Clearly keen to get the job done on the night, he rattled through the set with an astonishing display of power, getting 95 per cent of his first serves in and winning every one of his second serves.
Egter, Wimbledon’s curfew waits for no man, not even Kyrgios in full flight, and the match was on a knife-edge with the scoreline 6-4 4-6 3-6 6-1 3-3 when an SW19 official came on to court and called play off for the night.