The parents of the child, who was identified only as Lola in the French press, noticed something was wrong when she became weak and faint, France Bleu Isère reported.
They took the child to hospital where Lola was kept under observation for a few hours until she had recovered.
Doctors then allowed the family to return home. But later that evening at around 10pm the results of a blood test revealed that the baby had ingested cannabis.
A doctor at the hospital notified police, who then made their way to the family’s home to question Lola's parents.
When police arrived at the house they found the 22-year-old father in the process of rolling a joint.
Admitting that he had realised the reason for his child’s illness on their way to hospital, the father said that his daughter had ingested some cannabis that had fallen on to the floor.
As a precaution, the baby was taken back to the hospital where she was kept under observation for the night.
Social services are now investigating whether the parents are capable of looking after the child.
Earlier this year The Local Italy reported that a mother of three in Sicily was jailed after her toddler son was admitted to hospital with bruises, scratches, burns and a suspected cocaine overdose.