The proposal is one of 76 recommendations from an expert group looking at maternity services.
Caesarean sections should only be offered for clinical reasons, the review suggests.
Between three and five neonatal intensive care units across Scotland would care for seriously ill babies.
These would be supported by other special care units, the report said.
The review, announced in 2015 and chaired by NHS Forth Valley chief executive Jane Grant, has been examining best practice and current services.
The expert group's recommendations include:
Health Secretary Shona Robison said the proposals would improve a system that was already providing an "exceptional  maternal and neonatal service".
She said she hoped the recommendation on continuity of midwifery care would be adopted quickly.
"This move will help build relationship-based care between women and midwives, and will improve outcomes for women," she said.
"Changes to birth rate, demographics and best practice, as well as advances to clinical care, means the services we provide to women and babies must be adapted and updated.
"The clinical evidence shows us that, for the most critically-ill babies, delivering highly-specialist care in up to five enhanced neonatal intensive care units in Scotland will ensure better outcomes for them and their families."
Mary Ross-Davie, director for Scotland at the Royal College of Midwives, welcomed the report, describing it as a "defining moment" for maternity services.
She said: "The plan has the potential to revolutionise maternity care, to deliver safer and better services for women, babies and their families, and to improve the health of our population.
"What is so important is that this puts women and their families at the centre of care. The focus on continuity of care and carer - that is the woman seeing the same midwife or small group of midwives - is very welcome.
"There is very strong evidence that better continuity of care leads to better outcomes for the mother and baby."
Maternity services came under the spotlight last week when it emerged women in labour could not be admitted to a Glasgow  hospital due to overcrowding.
NHS Greater Glasgow and Clyde apologised after five women arrived at the Queen Elizabeth University Hospital and had to be diverted to other hospitals or had their planned procedures delayed.
The health board blamed a higher than normal number of admissions.
In November a BBC investigation revealed that Scotland's maternity hospitals recorded more than 25,000 adverse incidents since 2011.
The most serious cases included the deaths of 26 newborns and 79 stillbirths. Three mothers also died.

This article was about:
Pregnant women in Scotland should be allocated a primary midwife, providing care before, during and after the birth of their child, a review has found.