It is the first visit to Argentina by a Japanese prime minister in 57 years - the last was by Abe's grandfather Nobusuke Kishi in 1959.
Abe's one-day visit provides the latest big international encounter for Argentina's conservative president Mauricio Macri.
He has been working to boost Argentina's trade ties since he took office a year ago after 12 years of protectionist policies under his leftist predecessors.
Heading to Argentina after the APEC trade summit in Peru, Abe will meet businesspeople and members of Argentina's 65,000-strong Japanese community.
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The Argentine foreign ministry said the visit aims to reinforce ties "in the political and economic spheres and in trade, investment and cooperation in science, technology, culture and sport."
Japan's ambassador in Buenos Aires, Noriteru Fukushima, said in July that he wanted to multiply Japanese investment in Argentina over the next three years.
He said Japan aimed to increase investment to as much as USD 3.0 billion a year from its current level of USD 100 million.
"Currently bilateral relations between Argentina and Japan are very much focused on investment, above all on the auto sector, with the Honda, Toyota and Nissan factories," he said.
Japan has trading agreements with Brazil, Mexico and Chile, but not with Argentina.
Japanese exports to Argentina were worth about USD 1.2 billion in 2015, according to the Argentine state statistics institute.
That was twice the amount that Argentina exported to Japan.