The Iranian female team beat defending champions Morocco to win $10,000 in cash, Tehran Times reported.
Korea beat Côte d'Ivoire and came third and earned $5,000 in prize money.
A total of 69 athletes from the six countries competed in the World Cup Team Championships Series.
The World Cup Team Championships Series will be followed by the World Taekwondo Demonstration & Breaking Championships on Thursday (July 4) and the World Para Taekwondo Open Challenge on Friday (July 5).
The victory came a day after the Iranian male team completed a successful defense of the title on the first day and clinched the gold medal and $10,000 in prize money with victory against the hosts Korea in the final at the Air Dome at Song-Am Sports Town.
It marked a fifth consecutive triumph in the male event at the World Cup Team Championships Series for Iran, who dominated the competition and won their semi-final against Côte d'Ivoire in three rounds and the final against Korea in two rounds.
Korea had beaten both India and Morocco in two rounds to reach the final, and collected $7,000 in prize money for their silver medal.
Bronze went to Morocco, who beat Côte d'Ivoire over three rounds to earn $5,000 in prize money.
It was a successful opening day of competition in Chuncheon, which is hosting three premier World Taekwondo events this week.
MNA