Film director Michael Moore may have arrived on Broadway with the self-professed goal of taking down a sitting president.

But in the end, his politically liberal-minded show, “The Terms of My Surrender,” which closed this past weekend, failed to wow at the box office.

In its 13-week run, including a preview period, the show had ticket sales of $4.2 million, according to BroadwayWorld.com, a theater website that tracks grosses based on data from the Broadway League, a trade group. That figure represents only about 49% of the show’s potential gross.

Mr. Moore’s largely one-man production started on a strong note, taking in $456,000 in its first full week. But it quickly fell well under that mark, with ticket sales dipping below $300,000 in some subsequent weeks.

By contrast, Bruce Springsteen’s show, also largely a one-man affair, has taken in nearly 100% of its potential gross in two of its first three weeks. The rock star’s production, simply titled “Springsteen on Broadway,” already has grossed a total of $6.6 million, far eclipsing Mr. Moore’s show.

True to the billing, Mr. Moore’s production skewered Republican President Donald Trump. It also focused on Mr. Moore’s life and history of political activism.

In an email, Mr. Moore said the show was “the most artistically gratifying experience of my life.” He said there are “talks happening about taking this show on the road.” A spokesman for “The Terms of My Surrender” said a San Francisco engagement is being discussed for early 2018.

The spokesman didn’t comment on the budget of the production or if it made a profit or loss. The show’s lead producers are IMG Original Content and Carole Shorenstein Hays.

Theater-industry observers say reviews of the show, which mostly were negative, affected the box office. A critic for the New Yorker magazine said Mr. Moore “doesn’t have a late-night comedian’s timing. He punctuates his own jokes with nervous giggles, mumbles between lines, and, despite his baggy frame, has little sense of himself as a physical comedian.”

Moreover, observers noted that Mr. Moore wasn’t helped by the fact that many comedians already are offering that Trump-skewering perspective—without charging their audiences the price of a Broadway ticket.

“If you want to see something anti-Trump, you can just watch any of the late-night shows” on television, said Christopher McKittrick, an editor with Daily Actor, a website that covers theater.