New figures show a fall in sales, cash flow, investment, orders, turnover and profitability in the three months to the end of February.
Manufacturing comprises 20 per cent of the city region’s economy - compared to 10 per cent nationally - and a big part of its identity.
In contrast the service sector posted a rise in sales, orders, turnover and cash flow, but a fall in profitability.
The Quarterly Economic Survey figures were released at an EU debate organised by the region’s four chambers, with the University of Sheffield Management School, the Local Enterprise Partnership and RBS.
Sheffield Chamber president Jillian Thomas said a slump in oil prices, a strong pound, sanctions against Russia and a slowdown in China had all hit manufacturers.
But the EU vote was being felt for the first time.
She added: “There is no question manufacturers are postponing decisions due to uncertainty ahead of the referendum vote on June 23.”
Nationally, growth had fallen from 2.4 per cent to a predicted two per cent this year, she added.
“That’s massive, and I think it is very telling. I urge business leaders to understand what they are voting for and to make sure they vote.
“My great concern is that the referendum on Europe will be decided on migration and tourism and not on the economy and jobs.”
Bill Robinson, chairman of economics and regulation at KPMG, said the bookies were giving Brexit odds of two to one against - which translated as a one-in-three chance of the UK leaving the EU.
He added: “It would take at least two years to unpick the regulations. But it would be wise for you, your businesses and your shareholders if you have them, to do some preparation for Brexit now.”
Freight boss Ian Baxter said business leaders would be mad to throw away the EU’s free trade agreements which opened the door to 500m customers.
But Alex Story, of finance firm Wealth-X, said Britain was competing with 27 countries in the EU with 27 different demands.