Dixon said the referendum, which takes place on 23 June 2016, would have huge implications for the UK's architects and designers, for whom the EU is an important market.
A "Brexit" vote could potentially damage London's status as the world's design capital, he speculated.
But Dixon – whose company, Tom Dixon, trades extensively with the 28 member states of the EU – said people weren't talking about the consequences of a vote to leave.
"It's two months away and people really haven't woken up to it," he said.
When asked if uncertainty over the outcome was affecting sales of his products, Dixon said: "I think it is. It's hard to tell but I think people feel very nervous and people who feel nervous don't spend money on copper lamps. They won't build buildings."
Speaking to Dezeen at his food-themed installation in Milan this week, Dixon said that EU countries excluding the UK accounted for 30 to 40 percent of sales of his furniture, lighting and accessories. EU sales are growing by 15 percent a year, he added.
Yet he said it was difficult to get reliable information about how a "Brexit" vote to leave the UK would affect creative businesses, which generate £84 billion each year.
"I wish I could get some unbiased opinion and we're not getting that," he said. "What we're getting is really entrenched positions, for or against, that people are really reluctant to move from. I'm very confused."
Speculating on the impact of a vote to leave, Dixon said: "It could mean that people start manufacturing things [in the UK] again, which would be a good thing."
"Or it might mean that London becomes much more insular and stops being the international platform that it has become, which is really exciting for design."
He added: "We're facing a lot of really huge known unknowns and nobody really knows."
Even within his company, Dixon said there was a reluctance to think about the issue. "I keep on trying to bring it up [within the company] but people keep ignoring me, largely I think because they're terrified," he said. "It's a very, very complicated question with lots of consequences."
The EU referendum will ask voters in the UK whether they think the country should remain in the EU, or leave. The vote has sharply divided the country, with opinion polls at the time of writing showing no clear outcome.
Asked what he thought the outcome of the vote might be, Dixon said: "I’ve got this odd feeling that we might vote to go. Everything could change in the next couple of months."
Dixon, 56, founded the Tom Dixon brand in 2002. It was sold to a British investment firm earlier this year.