The Non-surgical Procedures and Functions of Medical Reviewers (Scotland) Bill includes a ban on under-18s having treatments, such as Botox and dermal filler, and requires procedures to be carried out in approved premises with a regulated healthcare professional on site.
The bill states that premises wanting to carry out procedures that pierce the skin like Botox and filler must be registered with Healthcare Improvement Scotland.
Advice Direct Scotland warned last year that people as young as 15 had sought support about botched Botox and filler treatment.
Overall, 430 people had contacted the consumeradvice.scot website for help over procedures that went wrong, with customers suffering a combined financial loss of £192,000.
The bill passed stage one with cross-party support following debate and is now making its way through Holyrood.
Jenni Minto, minister for public health and women's health, told Parliament: 'Non-surgical procedures have become increasingly popular, but regulation has not kept pace with this growing industry.
'Many people who undergo those procedures are happy with the results and there are many responsible practitioners operating in both the medical and beauty parts of the sector, many people value those procedures.
'This bill is not about restricting access or judging anyone who receives them. However, I have heard a number of powerful accounts of those procedures going wrong, including the tragic death in England of a young mother.'
If passed, Scotland will become the first nation in the UK to formally regulate non-surgical cosmetic treatments.
