Dr Watson, who won a Nobel Prize in 1962 for his part in discovering the structure of DNA, was due to speak at the venue on Friday.
But the museum has cancelled the event, saying his views went "beyond the point of acceptable debate".
Skills Minister David Lammy said Dr Watson's views "were deeply offensive".
He added: "They will succeed only in providing oxygen for the BNP.
"It is a shame that a man with a record of scientific distinction should see his work overshadowed by his own irrational prejudices."
| We feel Dr Watson has gone
beyond the point of acceptable debate
Dr Watson, currently director of the Cold Spring Harbor Laboratory (CSHL) in New York, has arrived in Britain to promote his latest book.
In an interview with The Sunday Times, the 79-year-old said he was "inherently gloomy about the prospect of Africa" because "all our social policies are based on the fact that their intelligence is the same as ours - whereas all the testing says not really".
He went on to say he hoped everyone was equal but that "people who have to deal with black employees find this is not true".
A spokesman for the Science Museum said: "We know that eminent scientists can sometimes say things that cause controversy and the Science Museum does not shy away from debating controversial topics.
"However, we feel Dr Watson has gone beyond the point of acceptable debate and we are, as a result, cancelling his talk."
The scientist has courted controversy in the past, saying that a woman should have the right to abort her unborn child if tests could determine it would be homosexual.
Dr Watson is also due to speak in Bristol at the annual Festival of Ideas which will be hosted by Eric Watson, Bristol University's vice-chancellor.
A spokesman for the university said it respected "freedom of speech and the right of people to express their views".
But it expected "some robust questioning of Dr Watson on his ideas".