The legislation, introduced across Scotland in May 2018, meant the cost of a unit could be no less than 50p.
Figures released on Thursday at the British Association for the Study of the Liver (BASL) conference show Glasgow has had a 21.5 per cent reduction in alcohol-related deaths from 2017 to 2018 - down from 186 to 146.
Matthew Cramp, BASL president, said: "This early evidence suggests that implementing minimum unit pricing does exactly what it is supposed to - it is a highly targeted measure that improves the health of the heaviest drinkers and those experiencing the most harm from alcohol whilst those who drink in moderation continue much as before."
Almost half (44 per cent) of the alcohol-related deaths in Glasgow last year occurred before May 2018, when minimum unit pricing was introduced.
Scotland was the first country in the world to implement a minimum unit price for alcohol, following a 10-year campaign by health bodies including the British Liver Trust.
It was then introduced by the Scottish Government, although the Scottish Lib Dems have called for the minimum price per unit to be more expensive.
NHS Health Scotland is leading an independent monitoring and evaluation programme for minimum unit pricing over five years.
Modelling suggests the legislation could save 392 lives in the first five years.
A Scottish Government spokeswoman said: "These findings from the BASL are encouraging.
"Preventing alcohol-related harm is a key priority for the Scottish Government and the 3 per cent decrease in alcohol sales between 2017 and last year, following the introduction of minimum unit pricing in May 2018, is very promising.
"We are still in the early days of this policy and the full impact of minimum unit pricing on harms will take time to feed through.
"Given the clear and proven link between consumption and harm, minimum unit pricing is the most effective way to tackle cheap, high strength alcohol that causes so much harm to so many families.
"We are confident minimum unit pricing will make a significant difference to the harms related to alcohol, including deaths."