"We know what has to happen," Cramer told "Squawk on the Street," suggesting Moonves must step down or be removed.
"This is an issue of conscience. It's an issue of morality. It's an issue of life. It's not an issue of stock," Cramer contended, pointing out Moonves acknowledged in a statement responding to Friday's report by The New Yorker that he "may have made some women uncomfortable by making advances."
Moonves also said in his statement: "Those were mistakes, and I regret them immensely. But I always understood and respected — and abided by the principle — that 'no' means 'no,' and I have never misused my position to harm or hinder anyone's career."
Asked whether Moonves deserves "due process" before judgment is rendered, Cramer said, "It's a 'statute of morality.' That's a higher 'statute,' an easier standard."
Cramer's comments were made one day after the CBS board announced its decision to seek outside counsel to investigate the allegations against the 68-year-old Moonves that date to between the 1980s and 2000s. The board, which made no decision about Moonves' role in the company, also postponed its annual shareholders meeting, which had been set for Aug. 10.
The New Yorker article, published online Friday, was written by Ronan Farrow, whose investigative reporting in October contributed to the downfall of Hollywood power broker Harvey Weinstein.
"All that we keep reading about is that the [CBS] board knew, the board knew, the board knew," Cramer said. If true, the board should have already been investigating the allegations, added Cramer, host of "Mad Money."
CBS was not immediately available to respond to CNBC's request for comment.
Shares of CBS opened higher Tuesday on Wall Street after Monday's 5 percent decline and Friday's 6 percent nosedive. The stock, as of Monday's close, was down about 13 percent for all of 2018.