Health watchdog ANSM on Wednesday said it had started proceedings against the Crinex laboratory to suspend sales of its Uvestérol D product "within the next few days" as a precautionary measure.
An investigation, launched after the baby died on 21 December, found a "probable link between the death and the administration of Uvestérol D", it said in a statement.
Health Minister Marisol Touraine called on parents not to give their children the supplement, while promising that substitutes would be found.
Vitamin D not dangerous
The problem appears to arise from the method of administration by pipette and not from the content, she said.
In 2013 the ANSM advised parents to give babies Uvestérol D before feeding.
The baby who died had already been fied and showed signs of suffocation immediately after being given the supplement, according to ANSM emails seen by the AFP news agency.
Uvestérol D has been under surveillance since 2006 due to several reports of problems, such as apnea and choking, with children who have been given it.
Crinex made the product more concentrated in 2014, thus reducing the dose, but the Prescrire review, which has followed the case, found no indication that the risk was reduced.
The company, which employs 27 people, specialises in prevention of illnesses in babies and oral hygiene.
Uvestérol D represented about 10 percent of its 20-millon-euro turnover in 2015.