JAKARTA, Indonesia—Divers searched for a Lion Air jetliner that crashed into the Java Sea carrying 189 people shortly after takeoff Monday morning from Jakarta, in what was the first major accident involving a new variant of the popular Boeing 737.

Some 30 divers faced a quick current in waters about 115 feet deep off the north coast of Java, the archipelago nation’s main island. By midafternoon, they hadn’t located the plane, a Boeing 737 MAX 8.

But...