American military chiefs allegedly devised the secret project, "A Study of Lunar Research Flights" - or "Project A119" - in the hope that the then Soviet Union would be intimidated by viewing the nuclear flash from the Earth, the Telegraph reported.
It would have given the US a much needed morale boost after the Russians successfully launched Sputnik in 1957, according to physicist Leonard Reiffel, who was involved in the project.
The US would have used an atom bomb, because a hydrogen bomb would have been too heavy.
The planning reportedly included calculations by astronomer Carl Sagan, who was then a young graduate.
Military officials, however, reportedly abandoned the idea, which would have taken place in 1959, because of fears that it would have an adverse effect on Earth, should the explosion fail.
The project documents were kept secret for nearly 45 years, and the US government has never formally confirmed its involvement in the study, the British daily said.
Instead of blowing up the Moon, the US intensified and eventually won the space race against the Soviet Union, with Neil Armstrong becoming the first man to walk on the Moon in 1969.