The Scottish Liberal Democrats highlighted figures showing at least 856 babies have been born with neonatal abstinence syndrome (NAS).
This means they showed signs of addiction because of their mother's substance use during pregnancy.
NAS symptoms include uncontrollable trembling, hyperactivity, blotchy skin and high-pitch crying.
The health board reporting the most cases was Lothian with 434, followed by Greater Glasgow and Clyde with 143 and Grampian with 118.
NHS Western Isles did not report any cases. Fife and Shetland said they were unable to provide the information.
Scottish Liberal Democrat leader Alex Cole-Hamilton, whose party obtained the figures using Freedom of Information laws, called them "utterly heart-breaking".
He said: "It is hard to think of a worse possible start in life for a new-born baby to have to endure.
“In 2016, the Scottish Government slashed funding to drug and alcohol partnerships by more than 20 per cent.
"Valuable local facilities shut their doors and expertise was lost, which has proved hard to replace.
"Scotland now has its highest ever number of drug-related deaths.
"The Scottish Government has belatedly begun to repair that damage, but there is so much more to do.
"It is time for radical action, not just to help people struggling with drug misuse today, but for future generations too.
"That means investing in local services which are best placed to intervene to stop lives from being lost and new lives starting dependent on substances.
“Drug misuse should always be treated as a health issue, not a criminal justice matter.
"Anything else will condemn many more children to be born into these awful circumstances.”
There were 1,339 drug-related deaths in Scotland in 2020, by far the highest rate of any country in Europe and more than three-and-a-half times that of England and Wales.
Nicola Sturgeon previously called the situation "indefensible" and "a national disgrace", and pledged to take action.
The First Minister admitted she and her Government had taken their "eye off the ball" on the issue.
A Scottish Government spokesman said: “Increasing investment in local services and providing support to women and families are central to the public health approach being taken in Scotland through our national mission to tackle the drug deaths emergency.
“The national mission is backed up with an additional £250 million to improve and increase access to treatment and recovery services for people affected by problem drug use.
"This includes direct funding of £3m per year to support families as well as £3.5m additional funding for services to provide support through the Whole Family Framework launched in December 2021.
“This Government has also agreed in principle to fund a National Specialist Residential Family Service, which will be run by the charity and housing association, Phoenix Futures, and based in Saltcoats, North Ayrshire to support single parents or couples along with their children.
"The service will also support women through their pregnancy and into motherhood.”