Andrew Cuomo proposed that possessing up to 25 grams of the drug in public view should be reduced from a misdemeanour crime to a violation, a less serious offence in state law.
His plan, which must be passed by the state legislature, should prevent more than 50,000 arrests made annually by police in New York City for the offence – more than for any other.
Thousands of these come after people are stopped for other reasons, under a controversial “stop and frisk” policy, and produce small amounts of marijuana after being told by police to empty their pockets.
This leaves them vulnerable to the charge of possessing the drug in public view. Concealed possession of such small amounts was reduced to a violation, which carries a potential $100 (£65) fine, in 1977.
Critics say the offenders, a disproportionate number of whom are young and from ethnic minorities, are being unfairly tarnished with a criminal record that makes it difficult for them to get jobs.
The possession of marijuana has been partially decriminalised in 14 states across the US, most recently in Connecticut last year.