The county, which includes health secretary Matt Hancock's constituency of West Suffolk, intends to axe 30 full-time posts, which according to Unite would be "highly damaging" for thousands of families, many of which are living in "vulnerable circumstances".
The move is in response to cuts to the council's public health grant which has been slashed by £5.47m since 2015/16.
Representatives of Unite - which includes the Community Practitioners' and Health Visitors' Association (CPHVA) - are due to meet council leaders today to ask them to reconsider the plans.
Internal council documents shown to a national newspaper reveal the council intends to make savings of around £1m by cutting its 0-19 "healthy services" budget by 10 per cent.
This could see the loss of at least 21 health visitor posts across Ipswich and coastal Suffolk, with other roles cut through redundancies and vacancies not being filled.
However, the union said the restructure could also prompt the remaining health visitors from its 120-strong workforce to look for posts in Cambridge, Essex and Norfolk, where pay and employment conditions were better.
The council's plans come as the latest figures from NHS Digital show the lowest recorded number of health visitors in England since 2012.
The union said there were 7,694 health visitors in England in January this year, a drop of 25 per cent since numbers topped more than 10,000 in 2015, when the Health Visitor Implementation Plan ended.
"These proposals are motivated by reckless cost-cutting and, if they were to go ahead, it would badly affect thousands of Suffolk families," said Mark Jaina, Unite regional officer.
Some of the health visitor roles would be replaced with staff nurse positions, and other administration and clerical jobs would be centralised in Ipswich, he added.
"The county council appears to want to sneak these plans under the radar without fully consulting all staff side organisations, especially Unite - we were only informed by our members," he said.
The union is concerned plans to replace health visitor roles with lower graded staff nurses would require external recruitment to fill the posts.
"There is already a chronic shortage of nursing staff, an estimated 40,000 across the country, so we are very concerned that the council will not be able to fill many of the roles it will need to advertise for," said Jaina.
The county council said it was consulting staff on proposals to deliver its provision for children and young people aged 0-19 after recently being awarded the contract to provide healthy child services for the county.
"This is an opportunity for us to remodel and improve our provision for children and young people aged 0-19.
"Among other suggestions, this includes an increase in school nursing provision by 34 per cent, building on the skill mix of those who work with children and families, and improving the digital offer, including a new helpline for parents who have questions or concerns.
"We're currently consulting staff on proposals to deliver the service within the funding that's available.
"This includes reviewing the work of health visitors and how this service can be improved," a council spokesperson said.
Meanwhile, the Lincolnshire branch of Unite has been balloting health vistors on strike action after it claimed the county council removed specialist elements from Level 1 training. The ballot was due to close on 27 June.