This happens as many commercial banks have lowered interest rates on gold deposits to nearly zero.
Eximbank said clients can send gold bullions to the bank from May 6, but they will not receive any interest.
The minimum amount of gold to be deposited is one tenth of a tael.
It is the first commercial bank in Vietnam that offers the service for free, Lao Dong newspaper reported.
In a separate move, the bank has encouraged gold depositors to switch to dong savings, offering to pay 0.15 per cent higher than market price for the gold. That compares to an extra 0.35-0.4 per cent at Viet A Bank, reported Thanh Nien.
The State Bank of Vietnam at the end of April had ordered commercial banks to stop lending gold and restrict deposits of the metal starting May 1.
It said the move is aimed to reduce the use of gold as currency.
Following the order, many commercial banks have lowered their interest rates on gold deposits to as low as 0.01 per cent a year. Dong deposits, on the other hand, can fetch interest rates of up to 14 percent per year.
Analysts have said as the habit of keeping savings in gold is still strong around the country.
They will even accept to pay banks to look after their bullion holdings, some analysts said.
The price of gold has risen nearly 38 per cent in Vietnam over the past year.
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