The pilot, running from Fenchurch, McMillan and Marfleet Family Hubs in Hull, provides eligible families with “quick, local access to free vitamins”, the council said.
It added the move would build on “two years of innovative work to increase uptake of the NHS Healthy Start, external scheme”.
Andy McKee, early help health co-ordinator at the council, said: “We know the Healthy Start scheme is incredibly important for families in Hull, particularly in areas of high deprivation.
“Our aim has been to take a whole-city approach, so families hear about the scheme from the people they already trust – whether that is health visitors, midwives, community workers or Family Hub staff.”
Hull City Council said it would continue monitoring the uptake of Healthy Start to “ensure families receive the support they are entitled to”.