According to sources, the actress is staying in a high-end confinement centre which charges $50,000 for a month's stay.
The centre, which is close to her home, boasts luxurious facilities and professional staff, including a hotel-trained chef who prepares the guests' daily meals.
The centre also reportedly values the privacy of its guests with strict security measures in place, which perhaps explains why the actress is willing to shell out the eye-watering amount.
Jun, who was last seen in public in October 2015, has been married for four years and announced her pregnancy last July.
Her husband, Choi Joon-hyuk, works at the Bank of America's Seoul branch and comes from a well-to-do family, reported Korean Herald.
He is the son of renowned designer Lee Jung-woo and the grandson of Lee Young-hee, one of the most respected hanbok (Korea's traditional costume) designers in the country. Choi's father runs one of the largest asset management companies in South Korea.
Jun's management company issued a statement shortly after the birth, which read: "After finally welcoming her eagerly-awaited baby boy, Ji-hyun and family are ecstatic. We hope everyone can give Ji-hyun and her new family their blessings. She will be seeing everyone again soon with her best work."
According to reports, Jun's next project will be a new drama by the same scriptwriter who wrote the highly-rated TV series, My Love From The Star, with actor Lee Min-ho rumoured to be the male lead.