The Mahle Engine Systems employee suffered a deep cut to his elbow as a steel coil was being handled near a bonding machine on 21 October 2014.
The Warwickshire-based firm admitted breaching health and safety laws.
The guilty plea came after a Health and Safety Executive (HSE) investigation found that there was no safe system of work in place covering the incident.
They also found that no suitable and sufficient risk assessment had been carried out for the task.
The HSE concluded that the accident could have been avoided had reasonably practicable precautions been taken.
The incident happened after an employee bypassed a machine guard in an attempt to connect the ends of a steel coil that was running through a machine designed to bond aluminium alloy to steel.
He was passing one of the ends of coil up to a colleague, who was standing above him on a gantry, when he was told by a manager to get out of the area.
When the employee let go of the steel coil, it slipped from the grasp of his colleague on the gantry and fell, causing a deep laceration to his left elbow.
Gary Aitken, head of the health and safety division at the Crown Office, said: "This was a foreseeable and avoidable accident which resulted in the serious injury of an employee.
"Mahle Engine Systems UK Limited accepted liability and the Crown accepted their guilty plea to the contraventions of the Health & Safety at Work Act 1974.
"Since this incident the company has introduced new risk assessments and has put into practice safe systems of work."
He added: "It is unfortunate that these long-standing issues were only dealt with following a serious accident and it is hoped that other companies learn from this incident."
A firm which manufactures engine parts has been fined £5,000 after a worker was injured at its plant in Kilmarnock.