Perhaps not at the individual level if that individual was raised in a culture which developed in a civilization that did derive morality from religion/God. That person would "inherit" their morality from their environment and heritage and then, if they turn out to not believe in God or have no religion, they believe that morality does not require God (since they do not believe in God but yet they are moral).
But, the better question is (assuming atheism and evolution are true): Would morality have come to exist (evolved) if humankind never developed/evolved the idea of God or religion? If so, how would it have been different from what we now call morality?
It seems to me that if morality did evolve (without God or religion) it would simply be a (complex) method of ensuring individual or group survival. So it would be reduced to a system of cost/benefit analysis and self interest. To me this is not morality.
So, a world that never had an idea of God could not be truly moral, just self-interested. In this way, I believe that morality requires an idea of God (but atheists can still be moral).