"Bill Maher's show will air as regularly scheduled Friday night," the cable network said in a statement Monday.
The network added that Maher will address his use of the racial slur during the program.
The comedian used the N-word during a conversation with Ben Sasse in which the Republican Senator invited Maher to "work in the fields with us," referring to his home state of Nebraska.
"Work in the fields? Senator, I'm a house n-----," Maher replied.
Sharpton wrote in part that his organization, the National Action Network, "wants to meet w/ HBO asap about the normalizing of the use of the N word. I know and love Bill Maher but this is unacceptable."
Chance the Rapper took it a step further. "Please @HBO Do Not Air Another Episode Of Real Time With Bill Maher," he wrote.
Both Maher and HBO apologized for the incident in statements released Saturday.
HBO said Maher's use of the N-word was "completely inexcusable and tasteless." The network added, "We are removing his deeply offensive comment from any subsequent airings of the show."
In his own statement, Maher said: "Friday nights are always my worst night of sleep because I’m up reflecting on the things I should or shouldn’t have said on my live show. Last night was a particularly long night as I regret the word I used in the banter of a live moment. The word was offensive and I regret saying it and am very sorry."