Bill Maher will not be benched for his comment about "house n*****" ... TMZ has learned.

Sources familiar with the situation tell us, HBO will not yank Bill from the air or fire him for the comment he made to Nebraska Senator Ben Sasse on last Friday's show.

Maher apologized quickly and the fallout from the comment got quickly lost after the London terrorist attack.

By the way ... the fact that HBO does not run advertisements makes the situation vastly different from networks that advertise ... HBO will not lose money because it's subscription-based and, realistically, very few people would unsubscribe. Maher's show will stand or fall on ratings.