The order further read, "Immigrants who enter this country should not further saddle our health care system, and subsequently American taxpayers, with higher costs".
Poland has long sought entry into the visa waiver program.
The order goes into effect November 3.
Critics have argued that President Donald Trump will struggle to implement his new plan to deny visas to immigrants who can not prove they will be able to afford health care within 30 days of entering the U.S.
The White House said in an accompanying fact-sheet that the President's order was meant to "ensure we protect the availability of healthcare benefits for American citizens".
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Poland had been one of just five European Union members whose citizens needed visas to travel to the U.S, which has always been seen as a thorn in otherwise cordial bilateral relations.
"This new attempt at an immigration ban is as shameless as it is stunning", tweeted Doug Rand, a former Obama administration official who is the co-founder of Boundless Immigration. The Trump administration said last month that it planned to allow only 18,000 refugees to resettle in the United States in the 2020 fiscal year, the lowest number in the history of the modern refugee program.
Under that policy, known as the "public charge" rule, immigrants seeking to live permanently in the United States could be denied if officials deem it is likely they will be a burden on society by, for example, being unable to pay for health care or seeking food and housing assistance.
The proclamation was announced Friday (Saturday in Manila).
As noted by Larry Leavitt, executive vice president for the Kaiser Family Foundation thinktank whose study is referenced in Trump's proclamation, lawful immigrants using Affordable Care Act's subsidies will also be stuck in a "catch-22" situation as subsidized coverage does not qualify as insurance under the proclamation.
According to the Migration Policy Institute, a nonpartisan immigration think tank, 57 percent of us immigrants had private health insurance in 2017, compared with 69 percent of USA -born, and 30 percent had public health insurance coverage, compared with 36 percent of native-born. The regulation, which imposes an aggressive wealth test on legal immigrants, has been delayed because of several legal challenges. "Consular officers will deny the parents of USA citizens based on a snap judgment about their apparent health".