SEOUL—A South Korean court denied an arrest warrant for Lee Jae-yong, the scion of the Samsung conglomerate, for his alleged involvement in a national corruption scandal, the latest twist in a saga that has shaken the country’s political and corporate establishment.

The Seoul Central District Court early Thursday rejected prosecutors’ application to detain Mr. Lee, saying that it had difficulty “seeing the reason, necessity, and appropriateness of an arrest at this stage,” adding that there wasn’t a sufficiently strong basis...