The study of 2,000 young people, who have completed or are currently in an internship, found only 27% received financial support to cover expenses during their placement, while 14% did not receive any payment at all.
Last week, prime minister David Cameron backed a campaign that aims to inform interns about their rights and employers' responsibilities. The campaign will encourage unpaid workers who feel exploited to report their employers to the national Pay and Work Rights Helpline.
Cameron said "exploitation of interns is unacceptable", but defended advertising unpaid jobs.
The study also questioned 285 recruitment and HR managers, and found that 22% who employ interns admitted to paying them less than the minimum wage.
Labour MP Hazel Blears, who has been leading the campaign against unpaid internships, said: "Unfortunately many of employers remain happy to get something for nothing when it comes to paying interns.
"I passionately believe these valuable opportunities should be open to all, not just to those from better off backgrounds who can afford to work for free."
Andrew Sumner, Monster's managing director of UK and Ireland, said: "A healthy economy relies on the investment businesses make in young people today. In such a tough economy, it is simply not acceptable there are still UK companies making interns work for free."
Earlier this year, Monster announced it will not support the advertisement of unpaid internships on its website.
