According to the TV channel, a group of hackers called Grief published 13 files on their resources and said that they had hacked the NRA.
Attackers are currently threatening to publish more files if the association does not pay the ransom.
Cybersecurity experts speculate that Grief is an attempt to rebrand the hacker group formerly known as Evil Corp.
The United States believes that this group is associated with Russia.
The NRA has not yet commented on the incident.
Earlier, CNN announced attacks by "Russian hackers" on US government websites.