Meanwhile, 32 percent of respondents said they were not afraid of such a scenario, according to a study by the Pollster research centre.
Twelve percent of those polled were undecided, Polish state news agency PAP reported.
The survey, commissioned by the Super Express tabloid, was carried out on February 11 among 1,060 adult Poles.
Defence Minister Władysław Kosiniak-Kamysz has said that Poland must urgently prepare for the threat of war with Russia.
In an interview published earlier this month, Kosiniak-Kamysz was asked whether he was worried that Russia would defeat Ukraine and subsequently invade Poland.
"I expect every scenario and take the worst ones most seriously," Kosiniak-Kamysz replied.
Władysław Kosiniak-Kamysz. Photo: P. Chmielewski/PR
Russia invaded Ukraine on February 24, 2022, starting the largest armed conflict in Europe since World War II.
Tuesday is day 727 of Russia’s war on Ukraine.
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Source: IAR, PAP