Clarkson, speaking at a press conference in Sydney, compared Mr Brown to Australian prime minister Kevin Rudd, after Mr Rudd had just addressed the country on the global financial crisis.
According to The Australian newspaper, he said: "It`s the first time I`ve ever seen a world leader admit we really are in deep s***. He genuinely looked terrified. The poor man, he`s actually seen the books.
"(In the UK) we`ve got this one-eyed Scottish idiot, he keeps telling us everything's fine and he`s saved the world and we know he`s lying, but he`s smooth at telling us."
Scots politicians reacted angrily to the remark. Scottish Labour leader Iain Gray said: "Such a comment is really a reflection on Jeremy Clarkson and speaks for itself.
"Most people here are proud that the Prime Minister is a Scot and believe him to be the right person to get the UK through this global economic crisis."
Gordon Banks, Labour MP for Ochil and South Perthshire, branded the comments "unforgivable".
The BBC and Downing Street declined to comment.
MOST PEOPLE HERE ARE PROUD!
Give us a break! If it wasn't for the sad passing of John Smith, we never would have had the worst double act in history. Blair & Brown.