Around 50 fans protested outside the County Ground after Saturday's 3-2 home defeat at the hands of Bradford City - with veteran Steve Claridge netting twice for the Bantams.
Reserve team coach Iffy Onuoura has been put in charge of the first-team on a caretaker basis.
King becomes the second League One manager to lose his job this season, after Brian Tinnion quit as Bristol City boss.