The shooting occurred just before 10pm on Friday at Torbett Street, with some media reports saying it started at around 9.45pm.
When officials reached the apartment, they found three dead and took the four who were wounded to the Vanderbilt University Medical Centre.
The injured are in stable condition, police said.
Police told local media that six members of a family were the ones who were shot. One of the two suspects, who entered the apartment after knocking on the front door, was also shot.
The two family members who were killed in the shooting were teenage brothers, according to the report. They were identified as 18-year-old Zacquez Sherrell and 15-year-old and Tavarius Sherrell.
Their 40-year-old mother, two sisters aged 16 and 20 and their 13-year-old brother were the ones injured in the shooting.
There was no sign of any forced entry into the apartment, according to Nashville police officials, who added that two guns were found at the scene of the crime.
Officials suspect robbery to be a motive for the shooting at the Nashville apartment.
Police said the two suspects went inside the apartment after knocking on the front door.
One of the suspects, identified as 29-year-old Christian Johnson, died in the shooting. WKRN-TV, an ABC affiliate, said Johnson was a convicted robber.
Kristin Mumford, a spokesperson for the police department, told the media that investigators were working to determine what happened prior to the gunfire, according to the WKRN report.
“We are pursuing some leads and also interviewing and talking to people. Anyone who may have left the scene or anyone who has information about what happened inside the apartment, we very much want to talk to you.”
Another shooting at a shopping mall in Durham, North Carolina left several people injured.