The motor was being hoisted over a hatch by Cotswold Lifts Limited when the incident occurred on 07 September 2010.
The impact caused structural damage to the concrete floor of the hospital lift lobby and to the ceiling of the level below.
A member of the public who was waiting for the lift was injured by falling debris and was admitted to Accident & Emergency.
Luton & South Bedfordshire Magistrates’ Court heard that the motor was being moved using a sling and block and tackle, but came loose and fell four metres.
An HSE investigation found Cotswold Lifts failed to properly plan and manage the operation, or make suitable arrangements to protect employees, hospital staff, patients and members of the public.
HSE served a Prohibition Notice after the incident to stop the company using the same approach and equipment to move other items.
Cotswold Lifts pleaded guilty to safety breaches and was fined £5,000 and ordered to pay £5,499 in costs.
After the hearing, HSE Inspector John Berezansky said: “Work on passenger and goods lifts is a high risk activity that causes significant numbers of serious and fatal injuries.
“The law broadly requires that competent persons plan, supervise and carry out lifting operations to ensure they are conducted safely.
“On this occasion Cotswold Lifts Limited failed to put suitable arrangements in place.
“Members of the public, including hospital staff and patients, had access to the danger area in the lift lobby below. It is a matter of good fortune that no-one was killed or more seriously injured when the metal motor came crashing down”.