Undergraduates from Nigeria fell by more than 14% in the same period.
Numbers from the three key countries fell by 1400 in 2011/12 compared to the year before, after the introduction of tougher visa restrictions by the Home Office.
It was sparked by widespread concern at the proliferation of bogus colleges operating as "visa shops". Scottish universities now fear they could lose as much as £23 million in revenue after the dramatic fall in students from the key countries.
Alastair Sim, director of Universities Scotland, said the decline, revealed in new figures from the UK-wide Higher Education Statistics Agency, was "deeply worrying".
Universities rely increasingly on the lucrative fees paid by overseas students to subsidise courses for home students – with charges as much as £17,000 a year for postgraduate courses.
They have recruited more students from countries such as China and the US this year to ensure numbers stay stable.
However, Mr Sim said India, Pakistan and Nigeria were "important markets for Scottish higher education and countries with which we have long-standing academic relationships".
He said: "It's very important that the message gets out to these countries that international students are welcome in Scotland. This is not the perception given out by hardline rhetoric from parts of the UK Government. It is telling that this fall occurred only months after the UK Borders Agency announced the end of its post-study work route that enabled international students to help pay off - fees."
Mr Sim said such work was still offered by many of Scotland's competitors and the loss of it had damaged the sector's ability to compete.
Graeme Kirkpatrickof NUS Scotland, which represents students, said:. "The UK Government's policies risk damaging Scottish education's international reputation for excellence.
"International students not only provide huge cultural and educational contributions to Scotland's college and universities, they make a huge economic boost to their local communities - The Home Secretary needs to urgently review these policies and ensure UKBA is not unfairly rejecting talented students."
A spokesman for UCU Scotland, which represents academics, said: "Many countries are now building huge new campuses for students who find it increasingly difficult to navigate tough immigration laws in the UK.
"It is particularly worrying that the Westminster Government does not seem to be aware of the damage these policies do to Scottish universities."
A Scottish Government spokesman said: "We have expressed concerns to the UKBA in the past around the difficulties that individuals from countries outwith the EU face when taking up a place at Scottish universities."
Last month, Home Secretary Theresa May announced consular staff would interview more than 100,000 prospective students to prevent bogus applicants entering the country.