SEOUL—South Korean prosecutors sought an arrest warrant Monday for Lee Jae-yong, the heir to the Samsung conglomerate, ensnaring the leader of the world’s largest smartphone maker in the country’s widening corruption scandal.

Mr. Lee’s arrest warrant, accusing him of bribery, embezzlement and perjury, must be approved by a South Korean court, which is scheduled to convene on Wednesday. An arrest warrant allows the specially appointed prosecutors to continue their investigation while Mr. Lee is detained. Formal charges and...