A similar number - 73 percent - are worried that the country’s healthcare system will be unable to cope and that hospitals will be overburdened, according to the study.
Just over one in four Poles - 26 percent - said that sometimes they feel so nervous about the epidemic that they are close to panic.
Meanwhile, 71 percent are worried the epidemic will trigger a financial crisis, the poll found.
Relatively few - 37 percent- are worried that shelves will be empty in shops.
The study was carried out on March 23 and 24 on a sample of 1,098 people by researchers from the Polish Academy of Sciences (PAN) and the University of Social Sciences and Humanities (SWPS).
The first case of COVID-19 infection was confirmed by Polish authorities on March 4, while the country's first coronavirus fatality was announced on March 12.
A total of 2,347 people have tested positive for the COVID-19 disease in Poland, with 35 deaths from the coronavirus so far, officials announced on Wednesday morning.