Firms could have to take their research and development work abroad in the future if home-grown talents are not nurtured, he warns.
Sir James says some 70% of engineering and technology post-graduates in UK universities are from overseas.
He says many take their expertise home with them when they finish.
The inventor and founder of the household appliance manufacturer, Dyson, highlights figures which shows how dominant overseas student are at post-graduate level in science, technology and engineering subjects.
“Of the additional 3,825 post graduate engineering students in 2008 only 70 came from the UK,” he says.
The figures are from a report he wrote last year on improving the UK’s potential for exports and are based on data from the Higher Education Statistics Agency.
“Although the number of students doing post-graduate engineering and technology courses has risen by a fifth over the past five years, the growth has almost all been made up of overseas students,” it adds.
Sir James told the BBC News website there would be a huge impact on the economy if this trend was not reversed and called for more government grants to encourage UK students to study postgraduate courses.
“We will be hamstrung without our scientists” James Dyson
“We [as a business] work with technology that is developed in British universities. If that’s not being done by English people then we can’t recruit them.”
This is because they often return overseas when they have finished their courses, he says.
“We will be hamstrung without our scientists,” he adds.
However the Department for Business, Innovation and Skills said postgraduate students were extremely valuable to the UK economy, and that the government provided considerable support to help them study.
“Around a third of UK and EU students on PhD courses in this country are funded by the research councils, who also provide help with living costs,” she added.
Sir James stresses that his own company carries out all its research and development in the UK and pays its taxes here, although its product assembly takes place abroad.
He currently has no plans to change this.
But he warns: “If we can’t recruit engineers and scientists here from universities – particularly those who have been on postgraduate courses – then we will have to go and recruit from foreign universities and locate our research in foreign countries.”
He says: “Now more than ever, the UK needs to create and export inventions the world wants to buy.
“As a nation we’ve become too scared to take risks, but it’s through experimentation and failure that new ideas are born.”
Universities UK said that at postgraduate level, in particular, the UK attracts large numbers of students from around the world.
“Around 40% of postgraduate students in the UK are international students and they sustain our research base in key areas.
“Almost half of our postgraduate research students are international, compared to one-third in the US,” a spokesman added.
Sir James argued that more students from the UK should be encouraged to stay on and take postgraduate courses and called for grants to help them do so.
“We should be actively encouraging people to be post-graduates and to take on doctoral work at university,” he said.
This could include increasing access to grants and loans from central government to help them do this.
Currently some postgraduates have to fund the tuition costs of the courses they study, although there are grants available from research councils and businesses that can help.
Fees are not regulated and are charged at the market rate. In engineering they range from £3,500 to £10,000 depending on the course of study and institution offering it.
Sir James also suggested higher undergraduate tuition fees could put even more students off staying on at university after they graduate.
He said: “If you have borrowed a lot of money to do your undergraduate course – you probably want to go out into the world and earn a salary money to pay that off.
“You are putting off the time when you can start paying back your loan and then you have to borrow money to do a post-graduate courses.”
He said there were concerns that postgraduate course fees could rise as universities tighten their budgets.
Paul Marshall, executive director of the 1994 group of smaller research intensive universities, said: “Post graduate students have so far been missing from the funding debate.
“While undergraduate students will be able to pay for tuition out of subsidised loans and a host of support measures, no such mechanisms are in place for those looking to study at a more advanced level.”
And he warned that post graduate courses are not going to be spared the impact of cuts to the teaching grant.
He added: “Put bluntly, course funds are going to be chopped without any support for students whose contributions will have to replace them.”
Sir James made his comments as he prepared to launch new business incubator units at the Royal College of Art’s new Dyson Building in Battersea – partly funded by the James Dyson Foundation – the inventor’s charitable arm.
He hopes the units will help encourage young inventors to follow their ideas in design and engineering.
By Hannah Richardson
BBC News education reporter