The provision taking effect Saturday requires checks by a licensed gun dealer, who can charge $10 and issue a form showing the prospective buyer passed.
Dealers already must use the FBI's National Instant Criminal Background Check System before they sell guns.
Federal law prohibits sales to many convicted criminals, people judged mentally defective, fugitives and illegal aliens.
New York's statute, enacted Jan. 15, immediately banned in-state sales of guns newly classified as "assault weapons" because of a single military-style feature, like a pistol grip on semi-automatic rifles with detachable magazines.
Other provisions effective Saturday require mental health professionals to report patients likely to seriously hurt someone and set tougher penalties for many gun crimes.