"The result is that our prisons are much safer and healthier places for Corrections staff," she said.
About 6000 inmates undertook nicotine replacement therapy in the months before the ban, with reports some had tried to smoke the patches to get their fix.
Before the ban, two-thirds of prisoners were smokers - triple the rate of smoking in the community - and smoking was the most common health risk factor among prisoners.
Ms Collins said many inmates entered prison with drug or alcohol addictions.
"If we're serious about helping them beat these problems we shouldn't have addictive substances of any kind in our prisons," she said.
Other countries, and most Australian states, had shown interest in how the policy was successfully implemented.
- NZPA