Senator David Leyonhjelm warned those who have incorrectly obtained a licence "could buy ammunition and gain access to a shooting range and shoot firearms on the assumption that you are a licensed person".
Service NSW said a total of 2,693 photo cards were sent to the wrong addresses this month, including the 104 gun licenses, 3000 drivers licences, 318 Mobility Parking Scheme Permits, 242 proof of age cards, 26 security licences and three commercial and private investigator licences.
"Service NSW apologises for the incident and we have moved quickly to resolve the issue by contacting the customers affected as soon as possible," a statement from the government agency said.
"The incident was a processing error and Service NSW has improved controls to continue to protect the information and privacy of our customers.
"The error is an isolated incident."