Garry Coutts urged Ms Scanlon to "support this radical legislation" in a letter that outlined his board's backing for the plans, which are due to be brought before the Scottish Parliament this week.
But Ms Scanlon, who is the Conservatives' spokeswoman on health and a list MSP for the Highlands, said the intervention, which was copied to health secretary Nicola Sturgeon and Labour's Shona Robison, was concerning and amounted to "campaigning on behalf of the SNP".
Mr Coutts wrote: "I am writing to urge that you support the Alcohol Bill and in particular the proposals for minimum pricing. You will be well aware of the cost that excessive alcohol consumption has on our society. This can be measured in long-term ill-health, social disturbance and cost in providing services."
He said his board believed measures should be taken to reduce excessive consumption of alcohol and added: "We are firmly of the view that only a minimum pricing strategy has the ability to do this."
Mr Coutts also addressed concerns brought up by political opponents of the policy, repeating claims made by the Scottish Government that minimum pricing would not affect the cost of branded whisky, beer or wine.
Ms Scanlon called for Mr Coutts to apologise: "He needs to be clear that this is not his job," she said. "Of course, politicians can be lobbied but not by someone in a position appointed by the Scottish Government and one which demands complete political neutrality."