The latest official figures from the National Records of Scotland shows 13,077 babies were born between July 1 and September 30 2018.
This is down 5.5% on the same period last year and is the lowest level for these months since civil registration began in 1855.
The previous low for quarter three was 13,200 in 2001, after which births rose again to around 15,500 by July to September 2008.
Since then births in these months have been falling and are now at 9.6 babies born per 1,000 of the population.
Statisticians believe there is no one reason for the drop in births but suggest possible causes could include women having children later, which often means they will have fewer, and the influence of economic uncertainty.
Compared to the quarter three average for the past five years, births have fallen 9%.
The provisional figures show the number of deaths dropped between July 1 and September 30 2018, down 4.2% on the same period the previous year to 12,625, giving a rate of 9.2 deaths per 1,000 of the population.
In the third quarter of 2018, deaths from heart disease were down 11.8% on the same period in 2017, while cancer deaths were down 1.3% and those caused by dementia and Alzheimer’s disease fell 5.2%.
Compared to the quarter three average for the past five years, deaths have dropped 2%.
Marriages also show a decrease, at 10,118, hitting their lowest level for the third quarter since 1943.
This is down 6.9% compared to the same period the previous year.
Same-sex marriages rose marginally by 1.1% to 373 between July and September 2018 compared with the same months the previous year, of which 23 were changes from civil partnerships.
Civil partnerships fell more than half, from 27 in the third quarter of 2017 to 12 in the same period in 2018.
Registrar General for Scotland Anne Slate said: “Numbers of both births and deaths were lower than the recent average for this time of year, although the fall in birth numbers is more pronounced.
“Continuing the downward trend since 2008, the number of births for the third quarter of 2018 is now the lowest number recorded since civil registration began.”