A typical definition of a "drug" is "a medicine or other substance which has a physiological effect when ingested or otherwise introduced into the body. "
Within that definition a vaccine is a drug, and is why the Covid vaccines are having to be reviewed by the licencing authorities.
And a general note for other posts:
Thalidomide was a wake up call to robustly review the effects of new medicines, and to days safety criteria would be very unlikely to approve Thalidomide without very strict prescription guidelines, and the same would be true for all other new drugs or treatments. The licencing process usually takes many months if not years, but becasue of the vital importance of a Covid vaccine has for global heath, the licencing process will be carried out as quickly as possible.
Even though the vaccines will be given priority consideration by the licencing authorities becasue of the global clamour for them, do not assume the licence will be simply rubberstamped through. If there are any concerns raised about safety, the licence may be refused or made conditional such as not to be prescribed for any groups identified as at risk.