He was among the first volunteers for the third phase trial of the vaccine.
The 67-year-old BJP leader was administered the dose at the Civil Hospital in Ambala.
He is the first Cabinet minister of any state government who has volunteered to take the trial dose.
Civil Surgeon Kuldeep Singh said the Covaxin dose was administered to Vij.
Before administering the dose, Vij underwent some tests at the hospital.
The minister told the media the vaccine likely to be available to the people by the beginning of next year.