The university has approved £4m sponsorship from the company which, it says, will be used to set up Britain's first International Centre for Corporate Social Responsibility.
Jon Rouse - who graduates on Thursday with a Master in Business Administration (MBA) - has asked for his £50 "student of the year" prize to be given to the Cancer Research Campaign.
In a letter to the head of the business school, Professor Ian Gow, Mr Rouse said he did not wish to accept the award because he did not agree with the university's collaboration with BAT.
The MBA graduate asked for a statement to be made at the graduation ceremony, outlining his stance.
'Richly deserve'
In his reply, Professor Gow said: "I am disappointed that you don't feel able to accept the award which you so richly deserve.
"But I respect your views on the university's decision to accept funding from British American Tobacco and understand that your decision is now made."
But it would not be appropriate for a statement to be made at Mr Rouse's graduation, the professor said.
"In fact the award is a business school one, which is completely seperate from graduation itself."
The presentation would have been made at a prize-giving tea in the business school after graduation, he said.
He would be happy to arrange for Mr Rouse to read a statement if he was intending to be present at the tea.
"We will reallocate the prize money as you request," the letter confirmed.
Regret
Mr Rouse said he was making a stand on a very important issue.
"I'm doing this with a great deal of regret," he said on Breakfast on BBC One.
"I had the year of my life last year at Nottingham Business School, it's a great business school, but it's just made a horrible error of judgement."
Mr Rouse said he thought the UK's universities had a very high standing - as President Clinton's visit to Warwick on Thursday illustrated.
Independence
"That's because they're independent and they are very objective," he said.
"As soon as you start having these sorts of relationships with companies with what can best be called a dubious track record, I think you're on a very sticky wicket."
Corporate social responsibility was not what came to mind when thinking of BAT, he said.
He hoped the university would pull out of the deal.
"I don't think it's too late, and I really think the business school should think very, very hard and reject the offer outright."