The young child had been given a dose of Uvesterol D, which is commonly used to prevent and treatment vitamin D deficiency in newborns.
But the baby later died on December 21 after suffering a devastating cardio-respiratory attack.
A statement from French agency ANSM said: “The conclusions of investigations so far show evidence pointing to a probable link between the death, and the dose of Uvesterol D that was administered.”
Now the brand, which is manufactured by the Crinex Laboratory, could be suspended from sale following an investigation.
Health Minister Marisol Touraine said: “I want to reassure parents who have given vitamin D, in any form whatsoever, to their children: They are safe.”
She called on parents not to give their child supplements of the particular brand, but promised other substitutes are fine to use.
The minister also committed to share “transparent, objective and reliable information” on the product as more data becomes available.
The suspension will come into effect in the next few days, and will only cover Uvesterol D administered with a pipette.
ANSM insisted the suspension was only a “precautionary measure” and confirmed other vitamin D products were still safe to use.
The agency had previously issued warnings about how the supplement was administered following a series of cases among infants, newborns under one month old, as well as premature babies.
The brand had also been under surveillance since 2006, due to several reports of problems including choking and apnea.
Corinne made the product more concentrated in 2014 and reduced the dosage, but a review found no indication that the risk to children was reduced.
Now the temporary ban on the product has sparked concerns across the globe about the safety of Vitamin D products.
However, the UK’s Department of Health recommends that children aged from six months to five years are given daily supplements – including vitamin D.
Dr Benjamin Jacobs of the Royal College of Paediatrics and Child Health in the UK said there were more than 100 products on the market used for young children – and that “side effects of vitamin D supplements are rare”.
Vitamin D, which helps address poor bone health, has previously been associated with conditions such as autism and asthma.