The announcement comes just weeks after HM Revenue and Customs launched an inquiry to investigate 100 companies believed to be breaking the law through their use of unpaid interns.
It is also in line with the bill that MP Hazel Blears proposed to make the advertising of unpaid internships illegal. This bill was later dropped.
Monster has become the first recruitment site to take this step. It says this type of work "exploits young job seekers".
Responding to the announcement, Blears said: "Too many employers are exploiting the hopes and dreams of young people by requiring them to undertake unpaid internships.
"This is unjust and unfair and excludes all those talented young people who cannot afford to live and work for free. It is time we all took action to stop this exploitation and I would urge other companies and organisations to follow Monster's lead."
Tanya de Grunwald, founder of graduate careers blog Graduate Fog and campaigner for fairer internships for young people, said: "For too long, seeing adverts for unpaid internships posted all over the internet has given both employers and young people the impression that unpaid internships are legal, which they aren't."
She added: "Worse still, these ads have constantly undermined the hard work that we campaigners are doing to raise awareness about the facts on unpaid internships."
