Athens is fast-tracking the legislation after ministers attended a medical cannabis trade fair last month.
The government last year authorized the import of several pharmaceutical products based on medical marijuana, as well as hemp cultivation for industrial purposes.
The draft legislation, if passed, would allow people aged over 21 and without criminal drug convictions to produce cannabis in Greece.
It is speculated that the legalization could open the door to overseas investors wanting to set up production in Greece.
Over a dozen EU countries have already authorized the use of medical cannabis.