Weymouth Magistrates' Court was told that employees of Carter Training had been using a mobile crane to lift a stillage of 500 2 kg fittings on a building site in Dorchester, Dorset.
The container turned on its side and the contents emptied on to staff working directly below.
The Health and Safety Executive (HSE) said that lifting equipment directly above contractors had put them at risk of harm.
The victim, 44, sustained two fractures to her left shoulder blade, a fracture to her left collar bone, a cut to the back of her head and bruising.
The HSE investigation found the stillage attachment used on the crane was not suitable for transporting large loads.
The principal contractor for the project and property development company Zero C Holdings had not audited the lifting plans and as a result had failed to manage the risks.
There were no clear lines of communication between the two companies and the contractors, the HSE found.
Zero C Holdings pleaded guilty to breaching reg 13(1) of the Construction (Design and Management) Regulations 2015 over its failure as the principal contractor to plan, manage and monitor the construction work. It was handed a £145,000 fine.
Carter Training, a provider of courses on construction plant and lifting operations and part of the Carter Group, admitted breaching reg 8(1) of the Lifting Operations and Lifting Equipment Regulations for failing to ensure that the job was planned, supervised and carried out safely. It was fined £18,000.
The companies were each ordered to pay £3,500 costs.
After the hearing, HSE inspector Nicole Buchanan said: "The worker is very lucky that her injuries were not life threatening. Both Zero C Holdings and Carter Training put a number of workers at risk of harm when they failed to plan or identify the risks of heavy lifting.
"Lifting directly above workers is inherently unsafe and should be avoided wherever possible."