Markets viewed Ishiba's top rival, Economic Security Minister Sanae Takaichi, as a more investor friendly option, analysts said.
The Nikkei was trading down 4.4% at 38,062.06 about an hour after the markets opened.
Ishiba has expressed support for the Bank of Japan’s efforts to raise interest rates after many years of keeping them near zero percent. That helped push the yen higher against the U.S. dollar, and exporters’ shares plunged, with Toyota Motor Corp. down 6.2% early Monday. Honda Motor Co.'s shares fell 6.8% and Nissan Motor Co.'s declined 5.8%.
A stronger yen is a disadvantage for Japanese companies that make a large share of their sales and profits overseas.
The future prime minister also has said he favors raising the minimum wage, allowing corporate taxes to rise and increasing taxes on financial assets.
Kishida espoused an economic policy he called “new capitalism,” which called for more equal distribution of national wealth. But sharply rising prices partly due to a weakening in the yen undermined progress toward encouraging consumers to spend more.
The dollar fell from over 146 yen to under 143 yen after the ruling party's vote ended late Friday. Early Monday it was trading at 142.65 yen, up from 142.29.