After political science student Noh Seo-jin finished class on Tuesday, the 19-year-old headed out for the last time to a campaign event with a yellow campaign jacket in her backpack and ambitions of becoming the Seoul city council's youngest member.

Noh is one of seven teenagers running for public office in South Korea's local elections on Wednesday, the first since the minimum age for local government council members and leaders was lowered in December to 18 from...