He issued the appeal amid anger and sadness among actors, musicians and other artists over the vote.
“In times of uncertainty and division it’s the arts that bring us together,” said Mr Vaizey. “London 2012 united the nation and the world looked on in awe of our creativity, courage and character. Now is the time to come together once more.”
Emphasising that the thriving arts scene was the “lifeblood” of creative industries, he said that Britain had to “seize on our strengths and look for opportunities”.
He said the arts had a vital role to play as “in many cases, they are what the rest of the world listens to, and what they know best about us”.
“They are naturally outward-looking, collaborative and internationalist. What they say matters,” he said. “They represent, after all, our most successful industries, and what they produce is the envy of the world. So it’s vitally important that the arts are given a voice in Brexit Britain, and I will be calling on every Conservative leadership candidate to ensure that’s the case.”
Meanwhile, leading figures revealed their fears. Golden Globe-winning actor Stanley Tucci said: “It’s a Mexit, it’s a mess really. I don’t understand why the British people have reached this decision, it saddens me.”
Harry Potter star Danny Mays, a Remain campaigner, said: “Culturally, economically, spiritually, the whole thing has gone to pot.”
Actress Jessica Hynes said: “Arts are what saves us in any situation, it explains things for us, it helps us to feel what we feel and it cheers us up and makes us feel better.”
Barry Ife, principal of the Guildhall School of Music and Drama, which before the vote released photographs of its symphony orchestra with and without EU students, said: “We are still a vibrant, tolerant, open and enthusiastically international country in spite of the impression that might have been given last week.”