Police said the 22-year-old man was injured when he became trapped between a digger and a gate at the building site of the new Waitrose supermarket at Foss Islands Road yesterday morning.
The man from West Yorkshire, who works for Leeds-based Howard Civil Engineering, remains in York Hospital with his family by his side, according to local newspaper The Press.
Wates is main contractor on the job where Howard is carrying out the groundworks.
A Wates spokesperson said the accident had happened at about 8.50am and the man was immediately taken to hospital.
He added: “The site has been sealed off and a Health and Safety Executive investigation is underway.
“We are cooperating fully with their investigation.”