It's one of 400 steps on the road to net-zero proposed by the agency in a special report.
The sale of new petrol and diesel cars around the world would end by 2035.
The IEA says that from now, there is no place for new coal, oil or gas exploration or supplies.
The report has been welcomed as an important contribution on the road to COP26 in Glasgow, when countries will attempt to agree the measures needed to put the Paris climate agreement into practice.
In that context, tackling the issue of how the world produces and consumes energy is the most critical endeavour.
The energy sector, according to the IEA, is the source of around 75% of the emissions of greenhouse gases that are driving up global temperatures.
To keep the world safe, scientists say that global heating has to be limited to 1.5C by the end of this century.
To keep close to that mark, emissions of warming gases need to drop by half by 2030, and essentially hit zero in 2050.
The IEA's new study sets out what it believes to be a realistic roadmap to achieve that aim, while at the same time creating millions of jobs and boosting economic growth.
By 2050 it envisions a global economy that is twice as big as today, with two billion extra people but with the demand for energy dropping by 8%.
The authors say their plan achieves this with no carbon offsets and a low reliance on technologies to remove carbon from the air.
Crucially, it sees no place for new supplies of coal, oil or gas.