A fine of $253,125 was imposed with reparation of $40,000 (including $10,000 consequential loss) ordered.
The worker was cleaning the chains used to move carcasses when her arm became trapped in the moving parts.
It took the victim's co-workers 10 minutes to help free her hand.
She suffered extensive lacerations and trauma to muscles, tendons, nerves, blood vessels and bones in her right hand and wrist. She may never have full use of her hand again.
Fresh Meats is a slaughter and processing company that processes over 250,000 lambs a year.
Adequately guarded machinery would have prevented the injuries, WorkSafe acting chief inspector Danielle Henry said.
"The importance of machine guarding has been a focus area across all industries for many years.
"Though a task instruction sheet prepared by the company clearly stated that machinery should only be cleaned when it was turned off, our investigation found it was common practice for staff to clean the machinery while it was moving."