The association will use the grant to identify the most effective ways Britain's 2,500 museums and galleries can "promote mental health and emotional wellbeing, and prevent mental ill-health".
"Museums are a huge untapped resource in contributing to the mental health of the nation," said Mark Taylor, the association's director.
The Big Lottery Fund made the award from its research grants programme.
"We considered the project to be an innovative 'seedcorn' study of how museums can contribute to the mental health of the population," said Nicola Osmond-Evans, a fund spokeswoman. "The case for the research was made clearly."
The research is to be carried out by the association's partner, the Campaign for Learning through Museums and Galleries, a cultural think tank.
The campaign believes museums can underpin people's mental resilience by providing access to social networks, offering safety and friendship in a neutral environment and building confidence and self-esteem.