The Labour leader said that all too often young people were being let down by a lack of adequate, easy to access services which maintained discretion on campuses.
Corbyn told a rally at Parliament on Wednesday evening: "Invest the money now, give the young people the support they need, they benefit, we as a society benefit."
He continued: "Down the line it becomes worse and much, much more expensive.
"We need to work with young people to stop mental health problems ever taking root.
"But we need also to educate those that teach, those that run our schools, those that run our colleges, and those that run our universities."
Touching upon the unique experiences of students living with mental ill health, he said: "It's very difficult for any young person to say to their peers that they suffer from depression. It's notoriously difficult in universities.
"As I travel around the country I visit a lot of colleges and universities, I always ask them what therapies are available, what support is available, how accessible is it, how confidential is it, and how discreet is it?"
Corbyn also hit out at the mainstream media, arguing its coverage of mental health rarely reflects the sheer scale of the problem.
He said: "Only a quarter of the children who experience mental illness get the help they need. In the UK, 60,000 people take their own lives and of those a third have mental health problems. The number of lives lost is rising.
"Have you read all that on the front pages of our national newspapers? Have you heard that on the mainstream media where it should be heard all the time?"
Meanwhile, the number of students seeking support for mental ill health is rising.
Writing on the Huffington Post UK, National Union of Students Vice-President Welfare Shelly Asquith has highlighted the growing need for well-funded mental health services.
She wrote: "The number of students seeking mental health support services is up by 132 per cent - services that are in many places undergoing cuts.
"Dismantling the grip of marketisation on education and its impact on our services and ourselves is necessary, but we cannot fulfill our aims if we continue to deny the very real effect it has on us, too."