North Korea has arrested three shipyard officials as it investigates the failed launch of a navy destroyer last week that badly embarrassed its leader, Kim Jong-un, state media reported on Sunday.

The chief engineer at the Chongjin shipyard on North Korea’s northeastern coast was arrested, as were the head of its hull-construction workshop and a deputy manager for administrative affairs, ​the official Korean Central News Agency reported.

Mr. Kim was watching as the shipyard tried to launch the newly built 5,000-ton destroyer ​on Wednesday, according to state media. Satellite images indicated that a large crowd had gathered for an elaborate ceremony to highlight Mr. Kim’s efforts to modernize North Korea’s navy.

But the ship lost its balance as engineers tried to push it sideways into the water. A satellite image taken after the accident showed the ship lying on its side, its stern in the water and its bow still stuck on the ramp. It was covered with blue tarpaulins, apparently to conceal it from spy satellites. (North Korea often carries out sensitive military construction under large canopies for that reason.)

Mr. Kim called the launch’s failure a “criminal act” and promised stern punishment, state media reported last week.

It was meant to be the North’s second launch of a destroyer in a month. The first, in April, at the Nampo port on the west coast, went smoothly; engineers set that ship afloat by letting water into a dry dock.