New documents show NHS Greater Glasgow and Clyde is battling to cover its massive case load in the face of 20 unfilled vacancies across the board area.
The papers repeatedly warn that health visitors are "working at full capacity and beyond", with bank staff being drafted in to plug gaps.
The health board has been unable to fill five posts because of a "poor response" to adverts.
The main role of health visitors is to check on new mothers and their babies in their homes to make sure they are developing normally and not at risk.
Matt McLaughlin, regional officer of health sector union Unison, said: "Even we were surprised by the picture that this report paints, to openly record that health visitors are working beyond capacity is incredible, this seems to suggest that NHS bosses are acknowledging that the current workload is unsafe for staff and unsafe for children and new mothers."
A spokeswoman for NHS Greater Glasgow and Clyde said an extra £2 million had been invested in health visitor services and funding was being put into training.
She said: "There is a national shortage of health visitors and, despite our best efforts, we have been unable to fill the current 20 vacancies we have in Glasgow. We are making every effort to recruit to these vacancies."
A Scottish Government spokesman added: "We expect NHS Boards to plan their workforce, including health visitors, to meet local population needs."