Lord Rees has lamented the crumbling state of Sir Isaac Newton's bust in London's Leicester Square.
The president of the Royal Society said the neglected sculpture was a potential symbol of Britain's future decline if science was undervalued.
In a speech to mark National Science Week, he said the fall in popularity of scientific disciplines as school and university subjects had to be arrested.
This was essential for the UK to remain globally competitive, he added.
The face on Newton's statue is horribly disfigured after an attempt to clean it with hydrazine, a chemical compound used in rocket fuel, went disastrously wrong.
Lord Rees, who is also the English Astronomer Royal, urged Britain to value better its scientific heritage and invest heavily in its scientific future.
"If we cannot recognise and celebrate the achievements of our best scientists, particularly in the physical sciences and engineering, then how can we expect future generations to follow in their footsteps, dreaming as much of winning a Nobel prize as of designing a landmark building?"
"We must ensure that to excel and become a world class scientist is an ambition that more of our young people pursue.
"Because if we don't inspire future generations to follow in the footsteps of the giants from our scientific past then Britain could quickly find itself overtaken by those countries that prize science more highly than us, and we would become an also-ran rather than a leader in world science.
"And the rather sorry-looking bust of Isaac Newton in Leicester Square will become a symbol of the decaying British position in science in the future, rather than merely a sign of our neglect of our outstanding past."
Lord Rees was speaking at a "Celebrating British Science" event, which highlighted the outstanding work of five post-doctoral scientists.
He emphasised the need for a sound science education for everybody, not just those intending to pursue a career in science.
"Today's young people, whatever career they choose, will all live in a world empowered by ever more elaborate technology - but also more vulnerable to its failures and misuses. There will be ever more political and ethical choices with scientific dimensions - nuclear power, the environment, and bioethics.
"So, science education is vital for everyone - not just for tomorrow's scientists, medics, and engineers. But as well as making education in science more open to all, we must make it more appealing to the vital minority of talented youngsters who will be the future of science in the UK.
"Our schools and colleges must inspire and prepare them, and our higher education institutions must develop their skills and knowledge, fit for jobs as researchers, technicians and indeed teachers and policy-makers."