Its public prosecutor's office said travelers arriving on international flights must disclose whether they have visited any of the red-listed countries affected by the Delta variant of the disease.
Failure to disclose this also entails severe punitive measures against them, it said.
A few days ago Saudi Arabia announced a three-year travel ban for its citizens who visit red-listed countries and territories as part of its effort to keep out the Delta variant which has been taking a heavy toll on many countries despite vaccination efforts.
The others in the red list are Afghanistan, Armenia, Belarus, the Democratic Republic of Congo, Ethiopia, India, Iran, Lebanon, Libya, Somalia, Syria, Turkey, the UAE, Venezuela and Yemen.
Saudi Arabia has had over 526,000 Covid cases and 8,249 deaths so far.
The highly transmissible Delta variant has become the most prevalent in many countries, including Vietnam where most new cases are linked to it.
Three months into its fourth wave, Vietnam has had 161,431 infections, including 1,846 deaths.