Mr Foster said he believed cheating was more prevalent among international students because some did not have good enough English language skills.
He described one overseas student scoring 2% in an exam and 99% in an essay.
"When you get that kind of disparity in the marks, it's clear the student has been cheating," he said.
"When you see a student who clearly struggled with the language and they submit an essay which William Shakespeare would have been proud of, then immediately that's going to arouse suspicion."
Mr Foster claimed many teachers "turned a blind eye" to cheating, which had allowed the problem to "snowball".
"Would you want to travel over a bridge that's been designed by one of these students?" he asked. "Would you like to put this accountant in charge of your business's operations?"
In a statement, Universities UK said the Home Office set the level of English required as part of the conditions for student visas.
"All universities have codes of conduct that include severe penalties for students found to be submitting work that is not their own," the statement added.


