The fatal incident is understood to have involved a pile driving machine at the Holmfirth site, although no further information has been released.
The 36-year-old man is believed to have worked for contractor PMC at the Ben Bailey Homes building site where steel pile foundation work was underway.
An HSE spokesman confirmed that it is carrying out a full investigation into the matter in conjunction with West Yorkshire Police.
A spokesman for the house builder said: “Ben Bailey Homes is currently working with the contractors, Greenpiling and the relevant authorities to establish the facts.
“Our thoughts are with his family and friends.”