The incident occurred shortly after 1pm on Thursday, March 28.
All three emergency services attended the scene and a police cordon was put in place.
The customer entrance was also cordoned off and the building closed to customers.
A spokesman for West Yorkshire Police said: "At 1.16pm today police were contacted by the ambulance service who were attending an incident at Paul White Ltd, in Upper Accommodation Road, Leeds.
"A man had been seriously injured while working at the site as a contractor.
"He was pronounced dead at the scene a short time later.
"His family have been informed."
"A scene has been put in place while enquiries are carried out into the circumstances.
"The Coroner’s Office has been informed."
The incident caused major disruption around the scene as emergency services attended.
Paul Wright, who works at a nearby plastics company in the building behind, said: “About half one loads of police and fire services turned up.
"There were four fire engines and a couple of ambulances - it was jam packed, they were mainly turning cars away.
“Most of them have gone now but for about 45 minutes it was ridiculous.”
A man who didn’t want to be named in the business next door, a pet centre, said: “We didn’t see or hear them turn up until we lifted the shutters at 1pm.
"We’ve been told nothing but with everybody here it’s looking like a tragedy.
“The guy who owns the business opposite has shut and gone home early because he’s within the cordon.”
Customers at a pub nearby explained what they had heard.
Angela Goldthorpe, a customer at the nearby Hope Inn pub, said: “At first we thought someone had been electrocuted but what we have been told is that a man was under the shutters and it’s gone and fell on him instantly.
“One of the workmen was trying to undo it and it’s released and fallen on him.”
Dawn Keenan, who was also at the pub at the time, said: “We were all wondering what had gone on and someone came and told us.
“Such a horrible thing to have happened. It must have been so instant - it makes you think. He could have had kids - I feel terrible for his family.”