Seiichi Eto, the minister in charge of Okinawa and what Japan calls "the Northern Territories" disputed with Russia, visited the shrine at the start of its annual autumn festival, an official at Eto's office told AFP.
Prime Minister Shinzo Abe meanwhile continued his recent practice of staying away from the shrine, instead sending a ritual offering, public broadcaster NHK reported.
The Yasukuni Shrine honours 2.5 million war dead, mostly Japanese, who perished in the country's wars since the late 19th century.
It also enshrines senior military and political figures convicted of war crimes by an international tribunal after World War II.
Visits to the shrine by government officials have angered countries that suffered at the hands of the Japanese military during World War II, particularly South Korea and China.
Relations between Tokyo and Seoul are already at their lowest point in years over a long-running dispute related to Japan's use of forced labour during the war.
The dispute has seen the two sides swap retaliatory trade sanctions, with the number of South Korean visitors to Japan plummeting in recent months.