In a letter to The Sunday Times, the AHA, wrote: "This policy will tackle head-on the problems caused by cheap drink, not only to drinkers but to those around them - the innocent victims of alcohol harm.
"Minimum unit pricing will target the heaviest drinkers: those who cause the most damage to themselves and others."
It added: "A child who lives with a problem drinker is vulnerable to neglect, violence and abuse, and a significant number of child protection cases are linked to alcohol.
"It is essential that the government stands firm in tackling problem drinking in order to turn the tide of alcohol harm."
More top news
A 16-year-old boy has been arrested on suspicion of terror offences as he prepared to leave the UK.
An man is reported to have wounded at least five people - two seriously - in an attack in the Swiss town of Schaffhausen.
Donald Trump's son-in-law has denied any improper conduct during four contacts with Russians during and after the presidential election.