The ministry said in a Twitter account statement that visa extensions would be automatic without any fees as part of efforts undertaken by the Saudi government in tackling the consequences of Covid-19 and mitigating its economic and financial effects.
Currently, Saudi Arabian authorities have banned arrivals from Vietnam and 12 other countries which are on the red list over the Delta variant.
Saudi Arabia had earlier announced a three-year travel ban for citizens who visit red-listed countries and slapped a 500,000-riyal ($133,300) fine on travelers coming from these countries as part of tougher measures to keep out the Delta variant.
Saudi Arabia has had over 535,000 Covid cases and 8,366 deaths so far.
Vietnam is currently facing its most challenging Covid outbreak so far, triggered by the Delta variant, which has prompted several countries to ban or impose stricter quarantine measures for travelers from the country.
In the ongoing wave that began in late April, the country has recorded over 242,000 cases.
The Saudi Arabian embassy in Hanoi last week donated around $500,000 worth of medical equipment to support Vietnam's Covid-19 fight. Since the beginning of this year, Saudi Arabia has provided Vietnam more than $800,000 worth of assistance for disaster relief and the Covid-19 fight.