Tate director Sir Nicholas Serota has said leaving the European Union would "diminish" the work of the Tate Modern.
The contemporary art gallery is re-opening to the public on Friday after a £260 million redesign.
Speaking in the Turbine Hall, Sir Nicholas told the Press Association: "I think that we all know that this is a museum that presents its face to the world, and it has enjoyed particular collaborations with European colleagues.
"We also know that we employ a large number of people here who come from other parts of Europe.
"Anything that makes that more difficult would, I think, diminish the quality of what we are able to show and do here."
Asked what he would do if there is a Brexit after the referendum on June 23, he said: "There's not really a contingency plan, we'll have to see what happens."
Lord Browne, chair of trustees, also emphasised the global nature of the Tate Modern.
He said: "At a time when some would seek to turn inwards, to dislodge this country from its rightful place in the global community, the new Tate Modern is a reminder of what can be achieved when we remain open to the world's ideas and cultures."
Ed Vaizey, minister of state for culture, communications and creative industries, said leaving the European Union would damage cultural collaboration.
He said: "I worry about leaving Europe. Clearly we have an engagement with our European neighbours, and we have a cultural engagement with them, and I'm sure to a certain extent that might continue.
"But it would send out, I think, a terrible message that we were turning our back on Europe, and I think art is about collaboration, the exchange of ideas, it's about internationalism.
"Here at the Tate we see an institution that's open to Europe and to the world, and we have millions of people coming here from Europe, for example, who think nothing nowadays of hopping across the Channel to see London's great attractions. And all of that would just become more difficult."
Mr Vaizey said the new Tate Modern's focus on geographical diversity and shifting the collection away from North-West Europe and North America was actually very British.
"I think it's fantastic, and I think weirdly because it's very global, it's very British," he said.
"I think the British are very good at understanding that we can be a platform for culture from all over the world. London is a global city, every country in the world is represented here."