Holt JCB instructed the apprentice to replace the machinery's air-filled wheels with foam ones on 8 April 2016, Swansea Magistrates' Court was told.
As he did, one of the 400 kg tyres fell on him and broke bones in both his feet.
An investigation by the Health and Safety Executive (HSE) found the company had failed to risk assess the job, had not trained staff on how to handle tyres, and did not have any wheel handling equipment at the site in Port Talbot, Wales.
Holt JCB pleaded guilty to breaching reg 4(1) of the Manual Handling Regulations, which requires employers to prevent workers from undertaking manual handling tasks which could result in them being injured.
On 1 June it was fined £67,000 in addition to costs of almost £3,000.
HSE inspector Steve Richardson said: "This incident could have been prevented in the company had used a mechanical wheel handler costing less than £700. Measures such as this would have been apparent had the task been properly assessed."
