Vaccinations in the EU are moving far slower than in Britain after the European Commission took charge of the procurement process.
In a video posted on his official Twitter page, Mr Farage said: “We could almost have a laugh about Ursula von der Leyen, clearly promoted way beyond her abilities.
“Trying on Friday night to impose a hard border between the Republic of Ireland and Northern Ireland.”
He later described the European Commission as “useless” and “bureaucratic”.
Last week the bloc threatened to introduce vaccine export controls after Anglo-Swedish drugs company AstraZeneca said it would be unable to meet its original order.
As part of this, Brussels triggered Article 16 of the Northern Ireland Protocol, creating a hard border between Northern Ireland and the Republic of Ireland, causing fury in London, Dublin and Belfast.
The EU later backtracked and said vaccine flows from Europe to Britain would continue uninterrupted.
Mr Farage used most of the eight-minute video to discuss the one-year anniversary of Britain officially leaving the EU.
Brexit formally took place on January 31, 2020 at 23:00.
The leading Brexiteer said: “I think because of Covid, because of 100,000 deaths, because of the misery so many people have been through we’ve sort of forgotten just how significant January 31, 2020 was.
“It was a massive historic day. A complete change in the direction of our country.
“I don’t know in the preceding 27 years just how many times I’d said the best people to govern Britain are the British people themselves but it was thousands and thousands.
“And I think what’s played out already over vaccines, we’re seeing the truth of that. A useless, bureaucratic European Commission.”
The UK is on track to vaccinate its 15 million most vulnerable residents by mid-February.
Appearing on Sky News’ Sophy Ridge on Sunday, international trade secretary Liz Truss noted Britain will end up with a vaccine surplus and indicated this could be used to support other countries.
She said: “What we know about the vaccination programme is this is a global problem and we need a global solution.
“We’re only going to be able to deal with this disease if we get everybody vaccinated across the world.”