The government minister, who is also a Christian, has been speaking at the PinkNews Awards.
While presenting an award, Mrs Morgan, who is also Minister for Women and Equalities, said: "I was shocked to discover that 1 in 10 social and healthcare staff have heard colleagues express the belief that someone can be cured of being gay.
"Let me be clear: gay cure therapies have no place in our countries and we must stamp them out."
Nicky Morgan's view on homosexuality has made news previously. She first voted against government proposals to legalise same-sex marriage but later changed her mind on the issue.
While therapy to help people change sexual orientation is legal in the UK, many counselling and health groups have spoken about the harm it can cause and have effectively banned their members from carrying it out.
But many Christian groups still promote the idea.
Speaking to Premier when a bill to ban this sort of therapy was brought to Parliament back in 2012, Andrew Symes from Anglican Mainstream said: "A lot of people are very concerned about this. It seems to be an attack on freedom.
"Many Christians believe that gay sexual relationships are wrong so what happens if Christians are same-sex attracted? They can be helped to live a celibate life but also there are many Christians who have counselling to investigate the possibility of changing orientation.
"It just seems that this bill is trying to deny that possibility to people."
The Government has made no commitment to tackle this issue and it's unknown whether legislation will be created.
Revd Peter Ould, a commentator on Christianity and sexuality told Premier's News Hour real evidence is needed: "If Nicky Morgan wants to ban any kind of therapy she actually needs to present the British public with some good evidence that it is harmful, that it doesn't work - if we don't have that evidence we can't do anything about it."
"Almost all the cases I know of people who sought to change their sexuality have been people who've chosen to do that.
"Now over in America we do have some cases of teenagers and young vulnerable adults who've been pushed - and clearly that's not appropriate, that's abusive."
Listen to Premier's Hannah Tooley speak to Revd Peter Ould here: