Portsmouth Crown Court heard how Martin Cox, 28, from Hayling Island, was injured after becoming trapped under the wall which he and six other men were attempting to lift.
The Health and Safety Executive (HSE) prosecuted the firms over the incident on the BAE Systems site in Broad Oak, Portsmouth, on 20 August 2008.
Principal contractor Emcor Facilities Services and Portsmouth-based subcontractor BS Interiors (South) had taken a decision to erect the 10.4-metre long, 2.8-metre high wall, flat on the floor due to the design of the building.
Once completed, seven workers, including Emcor employee Cox, attempted to manually lift the 1,136 kilogram timber, fibreboard and metal mesh structure into place.
When the lift was aborted, Cox was left trapped beneath the wall suffering dislocated ankles and fractures to his left foot.
He was hospitalised for two weeks and afterwards used a wheelchair for a year and underwent intensive physiotherapy. Two years after the accident he is not able to work full-time and still suffers pain and disability.
BAE Systems took on the role of Construction Design and Management co-ordinator, which meant they had to ensure that the design could be built without risks to the health and safety of those doing the building work. They failed to carry out any such checks.
There were also issues with the planning of the operation and manual handling of the wall that were not identified by Emcor Facilities Services.
Anne Bartlett, HM specialist inspector in occupational health, said: "This case illustrates the importance of identifying hazards at the planning stage. This is the key aim of the Construction, Design and Management Regulations 2007.
"If a proper risk assessment had been carried out, those involved would have realise that manual handing of the wall would have created a real and obvious risk to those present. It defies common sense and was extremely foolhardy.
"As a result for this failure, Cox sustained serious injuries that will affect him for the rest of his life, but which could so easily have been avoided."
BAE Systems Properties pleaded guilty to breaching Regulation 20(2)(c) of the Construction (Design and Management Regulations) 2007 (by virtue of Regulation 14(1) of the Construction (Design and Management Regulations 2007) and was fined £8,000 with costs of £6,110
Emcor Facilities Services pleaded guilty to breaching Regulation 22(1)(a) of the Construction (Design and Management) Regulations 2007. The company was fined £15,000 and ordered to pay costs of £6,110.
BS Interiors (South) pleaded guilty to breaching Regulation 4 of the Manual Handling (Operations) Regulations 1992. The company was fined £1,500 with no costs.