"The human race shouldn't have all its eggs in one basket, or on one planet," the renowned astrophysicist told the website Big Think, a forum which airs ideas on many subjects from experts.
"Our only chance of long-term survival is not to remain inward looking on planet Earth, but to spread out into space," he added.
He warned that the human race was likely to face an increased number of events that threaten its very existence, as the Cuban missile crisis did in 1962.
The Cold War showdown saw the US and Soviet Union in a confrontation over Soviet missiles deployed in Cuba, near US shores, and brought the world to the brink of nuclear war.
"We are entering an increasingly dangerous period of our history," said Hawking.
"Our population and our use of the finite resources of planet Earth are growing exponentially, along with our technical ability to change the environment for good or ill."
If we want to survive beyond the next century, "our future is in space", added the scientist.
"That is why I'm in favour of manned, or should I say 'personed', space flight."
His comments came after he warned in a recent television series that mankind should avoid contact with aliens at all costs, as the consequences could be devastating.