Mr Belfort's memoirs prompted The Wolf of Wall Street movie, starring Leonardo DiCaprio.
Mr Belfort was charged in 1998 with securities fraud and money laundering and served 22 months in prison after investors lost about $200 million. Investors are still chasing the full $110 million he was ordered to pay in restitution.
Asked if that was fair given she has no convictions, Prime Minister John Key said that was the reason there was discretion in some cases.
"The purpose of having an override by the officials is to deal with this very kind of example, that somebody who hasn't actually been convicted of something may still be worthy of being granted a visitor's visa to New Zealand."
Those ineligible for visas include people who have convictions, have been deported or refused entry to New Zealand or another country in the past, those considered a threat to security or public order, and members of terrorist groups.
Lawson, a celebrity cook, admitted taking the drugs during the fraud trial in January of two former aides who were acquitted of funding a luxury lifestyle with credit cards she and her ex-husband Charles Saatchi lent them.
Access denied
People who will "normally be refused entry permission" to New Zealand include:
• Those who have been "removed, excluded or deported from another country"
• Those who have been convicted and sentenced to five or more years in prison, or who have been convicted and sentenced to 12 months or more in the past 10 years.
- Additional reporting: Agencies