The Minack Theatre was visited by leaders’ spouses including Prime Minister Boris Johnson’s wife Carrie and US President Joe Biden’s wife Jill during the G7 summit.
In a tweet that has since been deleted, Mr Dowden reportedly said the outdoor venue had benefitted from the Government’s Cultural Recovery Fund (CRF), which aims to support the arts through the pandemic.
The theatre then rebuked the Cabinet minister in a reply on Twitter.
“Sorry @OliverDowden, but this is not true,” the tweet said.
“We did not benefit from any CRF money as we were not eligible to apply.
“It turned out having a good level of cash reserves meant we had to fend for ourselves and utilise our own reserves.”
A DCMS spokesman confirmed that an apology had been issued to the theatre.
He said: “Over 650 theatres have benefitted from over £250 million of support through our Cultural Recovery Fund to date.
“A tweet was briefly issued in error that the Minack was one of them and we have now spoken directly to the theatre who have accepted our apology.
“The Minack looked stunning yesterday as part of the G7 summit and we congratulate all at the theatre involved.
“The fund has made awards to more than 700 culture and heritage organisations across the South West worth up to £135 million, with funding decisions being taken by the Arts Council England, the British Film Institute, Historic England and the National Lottery Heritage Fund.”
After visiting the theatre on Saturday, Ms Biden tweeted: “Beautiful and powerful program for G7 spouses today at the @MinackTheatre.
“Thank you to Carrie Johnson and all those who helped put it together—especially all the local children who performed for us!”
The Minack Theatre, which is in Porthcurno near Lands End, is positioned on top of a cliff looking out to sea.