Meanwhile, 38 percent of those polled said they would welcome such a step, according to a survey by pollster CBOS.
Thirteen percent voiced the view that COVID-19 vaccinations should be mandatory for selected groups such as healthcare workers and teachers, state news agency PAP reported.
The survey was conducted from January 3 to 13 on a sample of 1,135 respondents.
In early December, the government announced plans for a vaccination requirement for doctors, teachers and law enforcement personnel.
Shortly before Christmas, Health Minister Adam Niedzielski published a draft regulation on compulsory vaccination against COVID-19 for medical professionals, pharmacists and medical students. The obligation is due to kick in on March 1.
A group of ruling party lawmakers in November submitted legislation to enable employers across the country to check if their staff are vaccinated against COVID-19.
As of Tuesday, Poland, a country of around 38 million, had injected more than 22.2 million first doses of COVID-19 vaccines, while over 21.6 million people had been fully inoculated, health ministry data showed.