The minimum fine can be replaced with a year behind bars, while maximum penalties are fines of four million shillings (about £30,000) or four years in jail.
The median annual wage in Kenya is just 80,000 shillings (around £600).
Nairobi has defended the harsh penalties by pointing to the way non-biodegradable bags are blocking sewers and choking waterways.
The UN environment agency says animals can be suffocated or poisoned by the bags.
Environment Minister Judi Wakhungu said manufacturers claiming the ban would hit jobs were off the mark, saying that the production of environmentally friendly bags would create jobs.
It follows action against plastic bags in many other countries. The UN says eight million tons of plastic is carried into the oceans every year, and that at current rates plastic will outweigh fish in the seas by 2050.