The academy said that nations were measuring their wealth by GDP (Gross Domestic Product), taking no account of the harm caused by business practises.
It urged countries to act as stewards of God's creation.
The statements are likely to influence the Pope's coming Encyclical on climate change.
An Cambridge Economics professor, Partha Dasgupta, told the academy's climate conference in the Vatican: "GDP is a disgraceful index because it does not count depreciation of our assets - including damage to Mother Nature, the most fundamental asset we have."
Cardinal Peter Turkson, who helped write the coming Encyclical - an official statement - said: "For humans to degrade the integrity of the Earth by constant changes in its climate; by stripping its natural forests; to contaminate Earth's water, land and air with poisonous substances - all of these are sins.
"There is an all-embracing imperative to protect our garden, our hope. We must move away from our unthinking infatuation with GDP."
The academy heard speech after speech urging the moral case for protecting the climate for future generations.
Meanwhile, a small group funded by a US climate contrarian body in Chicago has been in Rome rallying against the Vatican's climate drive. One of the participants, Christopher Monckton, said the Pope "should listen to both sides of the scientific argument... not only people of one, narrow, poisonous political and scientific viewpoint".
Inside the conference itself, the astronomer Lord Rees, former President of the UK's Royal Society, was putting just such a balanced view.
He acknowledged uncertainties over climate science, especially over how water vapour and clouds would react to warming.
He said some people were willing to bet on a low level of warming, mitigated later in the century by new technologies more affordable in a richer economy.  But, he said, the risks of triggering an irreversible catastrophe lasting thousands of years was too great.
"It would be shameful if our inheritance was a depleted and hazardous world," he said.
The Church is hoping to make an impact in a year of key UN meetings on Sustainable Development Goals, development finance and climate.
The Encyclical is expected to describe action to cut emissions as "a moral and religious imperative, highlighting the intrinsic connection between respect for the environment and respect for people - especially the poor, children, and future generations".
The Pope is hoping to build agreement among all religions on the moral obligation to protect the environment.
Bishop Marcelo Sanchez Sorondo, who heads the Academy, said the Encyclical would not be the highest level of proclamation from the Pope, which is reserved for issues of Faith.
But he said it was important for all the world's 1.2 billion Catholics to take it seriously. If any Catholic wanted to ignore it they would need "very good reasons - based not on personal or political opinion, but on science".
For some Catholics, this may prove an unwelcome Papal intervention into a highly politicised subject.
But the aid agency Cafod said its poll with YouGov showed the vast majority (70%) of Catholics say their community will heed the message of the Pope on climate change.
Whether it will prove persuasive for American Republican lawmakers - around a third of whom are Catholic - is yet to be seen.
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The Vatican Science Academy has challenged politicians to end their "infatuation" with a form of economic growth that is ruining the Earth.