Ms Inada is a close confidante of the Japanese prime minister with staunchly nationalist views. Mr Abe, who was reportedly playing golf, said he had “no comment” on her visit, Jiji Press said.
South Korea was quick to criticise Ms Inada.
“Our government cannot but deplore” the visit, foreign ministry spokesman Cho June-hyuck said in a statement, while in separate comments the defence ministry expressed “grave concern and regret”.
Ms Inada wrote in 2011 that Japan – the only country in the world to suffer atomic bomb attacks – should consider acquiring nuclear weapons.
In August after becoming defence minister she told reporters that Japan “should not consider arming itself with nuclear weapons at this moment”.
In 2014, she and another conservative lawmaker were seen in separate photographs standing next to the leader of a Japanese neo-Nazi party, though spokesmen for both denied any political affiliation.