The minimum age for varicella vaccine is 12 months. Vaccination is not recommended for infants younger than 12 months of age even as post-exposure prophylaxis. CDC recommends that a healthy infant should receive no specific treatment or vaccination after exposure to VZV. The child can be treated with an appropriate antiviral medication if chickenpox occurs.
See the Varicella Zoster Immune Globulin section for details on the recommended use of VariZIG in immunocompromised children, infants exposed to varicella around the time of birth and some hospitalized preterm infants.