Municipalities generate more than 63% of their revenue from electricity supply to households and businesses across the country.
Eskom and municipalities supply electricity in different parts of the country.
However, Eskom has in the recent times experienced problems of billions owed to it by several municipalities.
The power utility is owed more than R27 billion, and the overdue amount is R14bn.
Some of the MPs this week urged Mkhize to get Eskom to supply electricity directly to households and businesses and collect the money.
This would lead to the reduction of the debt due to Eskom by municipalities.
But Mkhize said this idea would leave the municipalities battling to stay afloat.
“The real issue is that municipalities use electricity as revenue. If you look at the revenue of municipalities it is 63%.
"If you say Eskom must collect directly and not involve municipalities it will shut down municipalities,” said Mkhize.
“We have seen collection in prepaid meters by municipalities is 99%. But in conventional meters by Eskom it is between 38% and 40%,” said Mkhize.
Former Eskom boss Brian Molefe a few years ago proposed in Parliament that the power utility must directly charge households and businesses electricity to reduce the municipal debt.
Molefe had argued it did not make sense to have municipalities supplying electricity to households and businesses, when Eskom can do that function and increase its collection rate.
At the time, Molefe said the idea had not been fully discussed at Eskom and raised with government.
When Pravin Gordhan was Co-operative Governance Minister, between 2014 and 2015, he warned that most of the municipalities were not financially viable because they didn't have a revenue base.
They were struggling to generate their own revenue leading to the merger of some of the municipalities.
Mkhize has also called for municipalities to generate their revenue to stay financially sound. Those with strong revenue streams must increase their revenue.
But Mkhize shot down the idea by some of the MPs of stripping municipalities of their powers to supply electricity and generate revenue.
Municipalities are in turn owed more than R139bn by households, businesses and government departments.
National Treasury has said in the past most of the debt was not recoverable as it was historical.
The debt has been increasing steadily from R49bn in 2010 to a staggering R139bn this year.