The private, non-profit museum said a sale of this type has never been done before in Brazil, although it is common in Europe and the United States.
The Pollock painting in question is titled “No. 16” and was completed in 1950.
Proceeds from the sale will be used to create a fund to keep the museum going for another 30 years, it said.
The painting is estimated to be worth around US$25 million (RM98.1 million).
The Brazil Institue of Museums called on the Museum of Modern Art to reverse course and try to come up with another way to raise money at a time of financial struggle for many of the South American country’s museums.
But the Culture Ministry said it supports the strategy, saying the Museum of Modern Art will become less vulnerable to economic crises and less dependent on donations and sponsorships.
Rio de Janeiro has been mired in financial turmoil since it hosted the Olympic Games in 2016, mainly because of a fall in oil prices. It is also suffering a hangover from the recession that all of Brazil endured in 2015 and 2016.