The SMF said the economy is predicted to require 104,000 graduate-level STEM jobs annually and currently has a shortfall of 40,000.
Its report, In the Balance: The STEM human capital crunch, uses the latest industry figures to analyse the mismatch between future employment requirements and the supply of home-grown skills in the STEM sector.
It states that, as the majority of the STEM jobs of the future will be in engineering, almost one in five 21-year-olds will need to be entering the engineering profession each year if the UK's young people are to meet demand.
The study reveals that just to replace an ageing workforce, a massive uplift in the numbers of UK STEM graduates is required in the face of a government clampdown on immigration.
To achieve the aims of economic rebalancing, the SMF said policy must focus on strengthening science and maths teaching at pre-GCSE level to boost home-grown skills by even more in the long-term.
Nida Broughton, senior economist at the SMF and author of the report, said: "The Government has made clear its aim to rebalance the UK economy towards manufacturing and away from financial services.
"But it has also pledged to reduce immigration. Our analysis shows the gulf between skills and jobs makes these aims incompatible in the short term."
Broughton added: "We're heading for a human capital crunch unless we can rapidly increase the numbers of young people taking science-related subjects at school".
The warning comes as manufacturing body the EEF yesterday released a report into women's representation in the industry and called for more to be done to "increase the pipeline" of female engineers.
The report found Europe is lagging behind the rest of Europe with nine out 10 engineers in the UK male.
The EEF believes the lack of female talent is due to a number of factors, not least the failure to encourage enough young women to study science related topics, which has left half of UK state schools with no women studying A-level physics.
To grow the pipeline of female engineers at all levels EEF believes there must be a national campaign to increase the number of women studying STEM topics to professional level, as well as to promote apprenticeships and other vocational routes into work.
To achieve this, careers advice must focus on promoting science and engineering options at a much earlier stage in school than key stages 4 (ages 14-16) and 5 (ages 16-18).
As part of the campaign, EEF has also challenged manufacturers to get more of its apprentices and manufacturing graduates involved in going back into their schools, colleges and universities to promote careers in industry.
EEF CEO Terry Scuoler said: "There is no getting away from the fact that women are substantially under-represented in manufacturing at a time when industry needs to be tapping into every potential talent pool to access the skills it needs."
