The victim is understood to be a subcontractor on the site run by a Costain/Galliford Try joint venture.
Sources told the Enquirer the victim was working for a drainage contractor and was killed by a site dumper.
The site is part of the JVs £65m scheme to boost capacity along the motorway between junctions 16 and 19.
A spokesperson for the Costain, Galliford Try joint venture said: “We offer our sincere condolences to the deceased’s family, friends and colleagues at this very sad time. An investigation is under way.”
Costain chief executive Andrew Wyllie sent an email to staff following the tragedy which was seen by the Enquirer.
It states: “I am very sad to have to inform you that a subcontractor colleague was fatally injured at junction 16 on our M1 smart motorways project site this morning.
“Our deepest sympathies go to his family, friends and colleagues.
“Our priority today has been to ensure the wellbeing and safety of everyone working on the site after today’s accident. A thorough investigation into this has started and a safety alert will be issued tomorrow.
“May I take this opportunity to remind everyone that our number one priority has to be the health, safety and well being of colleagues, clients and the communities in which we work.
“The tragic news we have had to share today reminds us all that we work in an industry where the risks to health and safety are high.
“Please do everything in your power to ensure everyone goes home safely at the end of the day.”