The rock star, 76, made his position clear in a statement as he asserted he would not play any stage to “a discriminated audience.”
Boris Johnson announced this week vaccination passports must be shown by those wanting to attend packed venues like nightclubs from the end of September.
But Clapton said he felt “honour-bound to make an announcement of my own” following the Prime Minister’s reveal on Monday.
“Unless there is provision made for all people to attend, I reserve the right to cancel the show,” he added.
The musician shared his statement via the Telegram account of Italian architect and Covid sceptic Robin Monotti, according to the Rolling Stone.
It was accompanied by a link to Clapton’s anti-lockdown collaboration with Van Morrison.
They sing “do you wanna be a free man or do you wanna be a slave?” in the track titled Stand and Deliver.
At least 42 Tory MPs have suggested they would not support vaccine passports.
However, Business Secretary Kwasi Kwarteng said he was confident the government would win but suggested it could just be on the “concept” of the vaccine passports.
“If the vote does occur, I’m confident the government will preserve a majority,” he added.
Currently, use of the NHS app to demonstrate whether clubgoers are vaccinated or have had a negative test is voluntary.
A Labour spokesperson said the party still needs to see the detail of what the government puts forward regarding vaccine passports.
He added: “We oppose the use of Covid vaccination status for everyday access to venues and services. It’s costly, open to fraud and is impractical.
“Being double jabbed doesn’t prove you aren’t carrying the virus. Testing for access to venues would be more efficient, and would give people and businesses more certainty.”
There have been suggestions the Prime Minister was using the plan as a way to boost the uptake of vaccines for younger people but No 10 appeared to dismiss this.
Speaking on Tuesday, Mr Johnson’s official spokesperson said: “This is the policy that the Prime Minister has set out and this is what we will be introducing by the end of September.”