The official, Jerry Matjila, told MPs in Cape Town that Swaziland needed the money to pay its civil servants.
South Africa's opposition said the request should be rejected because Swaziland was an "undemocratic state".
Swaziland is one of Africa's poorest countries and is governed by an absolute monarch.
Mr Matjila, who heads South Africa's International Relations department, said Pretoria was considering the request.
"The question is how much can we help. We want a stable continent. We start with our neighbours," Bloomberg news agency quotes Mr Matjila as saying.'Lavish lifestyle'
Kenneth Mubu Democratic Alliance spokesman
The king must reduce his expenditure which is a very big proportion of Swaziland's budget"
A spokesman for the opposition Democratic Alliance (DA), Kenneth Mubu, told the BBC's Focus on Africa that the government should not "prop up" the government of King Mswati III.
"It must first democratise, respect human rights and allow free political activity," Mr Mubu said.
He added that South Africa should also demand that King Mswati, who has 13 wives, end his lavish lifestyle as a pre-condition for aid.More