John Stankey, chief executive of parent company WarnerMedia, said that it was "in the best interest" of the firm that Mr Tsujihara steps down.
"Kevin acknowledges that his mistakes are inconsistent with the company's leadership expectations," Warner said.
The firm is conducting an investigation into the allegations.
Earlier this month, the Hollywood Reporter claimed an actress had sought Mr Tsujihara's help in landing roles after they had sex.
The report included text messages between Mr Tsujihara and the actress.
Mr Tsujihara's lawyer said at the time that the executive did not have a direct role in the hiring of the actress in any movie.
In a letter to staff on Monday, reported by Reuters, Mr Tsujihara did not address the matter.
"It has become clear that my continued leadership could be a distraction and an obstacle to the company's continued success," he wrote.
"The hard work of everyone within our organisation is truly admirable, and I won't let media attention on my past detract from all the great work the team is doing."
Mr Tsujihara had worked at Warner Bros for 25 years and had headed the studio since 2013.
In a statement, Mr Stankey said: "It is in the best interest of WarnerMedia, Warner Bros, our employees and our partners for Kevin to step down as chairman and chief executive of Warner Bros."
The company said that "it is working with a third party law firm to complete its investigation with Mr Tsujihara's cooperation".
WarnerMedia said it was yet to name a successor for Mr Tsujihara and declined to comment on a severance package.