Kim, who was received by Union minister Harsimrat Kaur Badal, will be the chief guest at the 'Deepotsav' event being organised by the Uttar Pradesh government on Tuesday.
On Monday, she will meet India's First Lady at the Rashtrapati Bhawan and will also call on Prime Minister Narendra Modi.
She will also meet External Affairs Minister Sushma Swaraj and attend an event at a school here.
Later, on Monday evening, she will leave for Lucknow where she will meet Uttar Pradesh Chief Minister Yogi Adityanath.
On Tuesday, she will leave for Ayodhya where she will attend the ground-breaking ceremony of the Queen Suriratna (Heo Hwang-ok) memorial.
"The First Lady's participation in the festivities in Ayodhya will showcase our close civilisational links as well as the ongoing deepening engagement between our two countries," the Ministry of External Affairs had said last week.
According to Korean legends, Princess Suriratna from Ayodhya had travelled to Korea and married King Kim Suro and became Queen Heo Hwang-ok some 2000 years ago.
The South Korean First Lady will also attend the 'Deepotsav' event in the evening on Tuesday.
Kim will leave for Agra on Wednesday for a visit to thee Taj Mahal before heading home.