They said the 26-year-old gave birth while at an Internet cafe in Seoul on March 25. She allegedly put the infant in a plastic bag, sealed it and dumped it in a nearby parking lot.
The woman had visited Internet cafes almost daily, police said.
"She was playing games until right before she gave birth in the cafe's bathroom," a police spokesman in the city's Songpa district told AFP.
"She didn't even know her waters had broken."
Police said the woman was being held in a state nursing facility and would face trial for infanticide.
There have been other reports of deaths related to Internet game addiction in South Korea, one of the world's most wired societies.
In 2010 a mother killed her three-year-old son while she was tired from Internet game-playing. Also in 2010, a 15-year-old boy committed suicide after killing his mother for scolding him over excessive playing of computer games.
A 41-year-old man was sentenced to two years in prison in the same year after he and his wife left their baby daughter to die at home of malnutrition while they were in Internet cafes.
Official figures estimate there are two million Internet addicts.
The government has adopted a "Cinderella" law to ban youngsters from playing online games past midnight as concern grows about Internet addiction