SEOUL—South Korea’s left-leaning government is planning to raise taxes on wealthy individuals and large companies, the first increase in the country’s corporate-tax rate since 1991, as President Moon Jae-in seeks to fund a massive expansion in public-sector hiring.

The move by the three-month-old government bucks the prevailing global trend of falling corporate tax rates. Countries such as the U.S., France and the U.K. have either slashed or have considered lowering rates in recent years in a bid to boost competitiveness...