Without the fix, various transistors could overheat, which could force the car to shut down, the Wall Street Journal reported.
The Prius cars involved in the recall were made in 2009 or more recently.
It is the largest recall every involving the Prius, which was first made in 1997, the Journal said.
The software problem has not resulted in injuries, but the company has received hundreds of complaints.
In spite of the number of complaints -- 451 since May 2011 -- the recall may signal a turning point for vehicle recalls given the increasing complexity of their computerized systems, the Journal said.
"Car makers need to bring together their wisdom to avoid recalls as they use more electronic parts ... and try to share these parts," said Hiroshi Ataka, an industry analyst at IHS Automotive.
Complex electronic systems may also make it harder to diagnose a problem, Ataka said.
The recall involves close to a million cars in Japan, 713,000 in North America and 130,000 in Europe, the company said.
Attkisson leaves CBS News, reportedly over network's 'liberal bias'
LGBT community has 'bullied the American people': Bachmann