The worker was employed by Billington Structures who are a subcontractor on the site where McAlpine is building a £25m paint plant for BAE Systems.
A McAlpine spokesperson said: “Sir Robert McAlpine can confirm that a mobile crane driver on its BAE Systems’ site in Barrow in Cumbria was injured following a fall yesterday (Wednesday).
“The worker is employed by Billington Structures, one of Sir Robert McAlpine’s subcontractors on the site.
“The emergency services were called immediately and the worker was transferred to hospital.
“The safety of all our workers on site is Sir Robert McAlpine’s highest priority and together with Billington Structures we have started an investigation into the cause of this accident.
“We cannot provide any more information at this time.”