The movie, a subversive take on the building-block toys, collected a disappointing $35 million in the U.S. and Canada, according to preliminary box-office estimates. It is an opening that could signal that the “Lego Movie” franchise—once considered a prime asset for the AT&T Inc. studio—has lost its luster.

“What Men Want,” a new release starring Taraji P. Henson as a woman who suddenly can read men’s thoughts, opened to a healthy $19 million. It was released by Viacom Inc.’s Paramount Pictures.

“Cold Pursuit,” the latest Liam-Neeson-on-a-mission thriller, failed to warm many seats and grossed $10.8 million. It was released by Lions Gate Entertainment Corp.

Since the original “Lego Movie” grossed $258 million in 2014, the franchise has steadily declined in performance. That is likely due to oversaturation in the market: Warner Bros. released two spinoffs of the series in 2017 alone: “The Lego Batman Movie” and “The Lego Ninjago Movie.”

“Lego Batman” collected a robust $176 million, but “Lego Ninjago” grossed a disappointing $59 million. Box-office analysts expected “Lego Movie 2” to perform better than it has since it is a sequel to the original film and not a spinoff like the others.

After a record-setting year at the box office in 2018, Hollywood suffered its worst January in eight years. The early months are always a slow time for the industry, but last month saw several bombs, including “Miss Bala” and “The Kid Who Would Be King.”

Audiences gave “Lego Movie 2” and “What Men Want” an “A-” grade, according to the CinemaScore market-research firm.

That positive audience response to “Lego Movie 2” could help Warner Bros. recover in the weeks to come. The previous installment pulled in audiences at a healthy rate following its debut, said Jeff Goldstein, Warner’s president of domestic distribution.

On the sequel, “it looks like we’ll have a big multiple even though we opened at a lower level,” he said.

Write to Erich Schwartzel at erich.schwartzel@wsj.com