Jonghyun, full name Kim Jong-hyun, was one of the five members of Shinee, who have had a string of number one hits in their home country.
The Korean Herald said he was 28 years old. He was taken to hospital after being found unconscious in an apartment in Seoul, according to reports.
Police told the BBC Korean Service that suicide will be investigated as a possibility.
Emergency services were alerted by the singer's sister and he was later pronounced dead at hospital.
The AFP news agency said his sister raised the alarm after receiving a number of text messages from her brother, including one saying "this is my last farewell".
As well as being a singer and an accomplished dancer, he played a large part in the group's songwriting and production, and launched a successful solo career in 2015.
He has also made headlines for voicing his opinion on issues like the government's education policy and for speaking out in support of LGBT rights.
Shocked fans have been paying tribute on Twitter.
Shinee's dance-pop has also been big outside South Korea. The group have recorded a string of Japanese-language albums and sold out the 55,000-seat Tokyo Dome.
In the UK, Odeon's website crashed a minute after tickets became available for their appearance at the Korean Film Festival in London in 2011, and they played their first North American tour earlier this year.