Members of the joint health and education select committee were told that withholding the top rating for poor performers on mental health would ensure schools put in place measures such as early identification of problems, improving teachers' mental health awareness and supporting pupils who have a mental health crisis.
YoungMinds chief executive Sarah Brennan told MPs the move would be "controversial" but said it was needed to address "patchy" provision of mental health support in schools.
"As much as we are very conscious that we don't want to increase the burden on teachers and on schools there does need to be a rebalancing here because we are ending up harming our children and we need to do something to improve the mental wellbeing of our young people," she said.
Another expert appearing before the committee group, Professor Sue Bailey, chair of the Children and Young People's Mental Health Coalition, said improvements to the way Ofsted inspects schools are needed if a heightened focus on mental health in inspections is to be effective.
She called on inspectors to mirror strategies deployed by businesses, which regularly assess the mental health of staff, and in the health sector, where more detailed, probing questions are asked.
"Now is a really timely opportunity to bed in how they [inspectors] will measure for mental health and wellbeing. You need some probing questions like can pupils explain accurately and confidently how to keep themselves healthy?
"Can they make informed choices about healthy eating, fitness and emotional wellbeing?"
"This needs to be dynamic and 24-hours-a-day, five-days-a-week so that people can see where [inspectors] are approving and where things are building up.
"That is what business and industry would do. There are lessons to be taken from industry in this case to measure wellbeing," she said.
Brennan said Ofsted would also need to review its inspection framework to see what areas of scrutiny can be reduced to ensure a heightened focus on mental health support doesn't overburden schools and teachers.
Emily Frith, director of mental health at the Education Policy Institute, said she is concerned that currently Ofsted inspectors may lack the skills to effectively measure mental health.
"The benefit of Ofsted looking at wellbeing is that it is a signal to schools that it is part of their job," she said.
"But there are dangers involved. There are risks if you think Ofsted is the answer then it is just about being a tick-box exercise. There is also the risk that Ofsted inspectors will not have the skills and capacity to look into this in enough detail," she said.
MPs were also told that offering badges of accreditation could help to improve mental health support in schools. Brennan said: "Getting a badge for being an outstanding wellbeing school would be attractive."
The joint health and education committee is conducting an inquiry into the role of education in children and young people's mental health which is looking at the role of schools and colleges in promoting emotional wellbeing and preventing mental health problems.
It is also exploring the skills of professionals in this area and the role of social media and the internet in young people and children's mental health.
Last May the government announced that more schools would join a programme of joint working with child and adolescent mental health services (CAMHS).