A local detective told AFP news agency that the intruder was attempting to steal valuables and had been detained on charges of aggravated robbery.
The suspect reportedly threatened both women and demanded money after breaking into the house.
Nana and her mother called the police after restraining the man, who was also taken to hospital for treatment, local media said.
Nana rose to fame in 2009 with the popular K-pop girl group After School.
The group is no longer active but she has since gained popularity over the past decade as an actor.
She has starred in several TV series, including Kill It and Justice, both crime dramas which first aired in 2019.
Nana released her first solo album in September.