The kingdom recently recorded a surge in infections, prompting authorities to urge the public to follow health and precautionary measures, including social distancing and the wearing of masks.
The ministry said vaccines were given at more than 587 sites across the kingdom as it reported nine new deaths and 948 infections on Saturday.
Vaccines are available to all citizens and foreign residents for free, the government said.
Authorities imposed fines of up to 200,000 riyals or a jail term of two years, or both penalties, for those who violate their quarantine regulations.
Since the outbreak of the virus in March last year, the kingdom has recorded a total of 404,054 cases and 6,810 deaths.
Before the vaccination drive began, the Health Ministry said it hoped to have enough to cover 70 per cent of the population by the end of this year.
Saudi Arabia has a population of about 35 million people. The kingdom approved the AstraZeneca and Moderna vaccines in January to speed up the inoculation campaign.
Prior to the new year, the Pfizer-BioNTech vaccine was in use. Those wishing to get a vaccine can do so by applying through the Tawakkalna mobile app.