Coutts, the prestigious private bank for the wealthy, the BBC has been told.
It is understood that he was subsequently offered a standard account at NatWest which owns Coutts.
Mr Farage says he believes his account is being shut for political reasons and he has been turned down by nine other lenders after trying elsewhere.
But people familiar with Coutts' move said it was a "commercial" decision.
"The criteria for holding a Coutts account are clear from the bank's website," they told the BBC.
Coutts requires its customers to borrow or invest at least £1m with the bank or hold £3m in savings.
Speaking to the BBC from France, Mr Farage did not dispute the fact that he did not meet Coutts' threshold, but added: "They didn't have a problem with it for the last 10 years."
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