The Liberal Democrat Chief Secretary to the Treasury, who acts as the chancellor's deputy, made the comment as he dismissed calls from the Tory benches for a pre-election reduction.
David Cameron has fuelled speculation by repeatedly refusing to rule out a further trimming the current 45p rate for those earning over £150,000 a year. It fell from 50p last year.
But in an interview with the Daily Mirror, Alexander said: "I think it is right at 45%. I wouldn't go to cutting below 45%.
"I would say that would happen over my dead body.
Asked about Cameron's refusal to rule out cutting the top rate, he replied: "You'll have to ask them (the Tories) why they answer those questions in those ways.
"If you ask me would I cut the top rate below 45p the answer is 'no'. In this Parliament we will not allow that to happen." Alexander also had some praise for Labour's Ed Balls - amid questions over whether the Lib Dems could work with the party in a future coalition.
"I play cricket with Ed Balls. I have opened the bowling at Lords while he kept wicket behind the stumps and I have to say he didn't let anything past him. So I would endorse him as a wicket keeper," he said.
London mayor Boris Johnson repeated his call for the rate to be cut to 40p - and declined to rule out the possibility of it happening before the general election.
"The last thing I want to see is a pointless sacrifice from the Liberal Democrats, let alone the dead body of Danny Alexander," he told BBC Radio 4's Today programme.
"Sooner or later there will have to be a new Conservative manifesto and I can't believe we are going to go into an election on a campaign to keep our tax rates higher."
Asked if that meant he accepted it could not happen until after 2015, he said: "Who can say what will happen to Danny Alexander? Stranger things have happened at sea.
"I don't think that it is reasonable always to keep UK tax rates higher than those of competitor countries.
"UK income tax is now higher than the average in the EU. That never used to be the case. I don't see why it should be the case for the long term and I see no reason why we shouldn't bring it down."
Chris Leslie, shadow chief secretary to the Treasury, said: "Danny Alexander seems to have forgotten that just 10 months ago he cut the top rate of tax for the top 1% of earners. And that was after saying anybody who wanted to do this was living in 'cloud cuckoo land'.
"After cutting taxes for the richest while breaking their election promise by raising VAT on everybody else, nobody will believe a word the Lib Dems say on tax.
"Labour will reverse this tax cut for millionaires as we balance the books in the next Parliament in a fairer way. It tells you everything you need to know about David Cameron and George Osborne that they haven't ruled out cutting the top rate of tax again."