The International Monetary Fund forecasts Poland will grow by only 1.3 percent this year, down from a peak of 7.1 percent in 1997 and 2.0 percent last year.
Meanwhile, Ireland, the second country to receive an EU bailout after the 2008 financial crash, is expected to grow by a similar 1.1 percent.
"Poland has collapsed," said Nicholas Spiro of Spiro Sovereign Strategy, on Monday. "It has a huge domestic economy, but essentially domestic demand has been contracting. It is being propped up entirely by exports, so all eyes are on Germany to see if the German economy recovers."
(Read More: Germans Among the Poorest in Europe: ECB Study)
Poland's flash gross domestic product for the first quarter came in at 0.4 percent year-on-year on Tuesday, below the 0.7 percent forecast by economists polled by Reuters.
Peter Attard Montalto, an emerging market economist at Nomura, said the disappointing numbers suggested Poland could post even weaker growth in 2013 than the IMF predicts.
"Poland's flash GDP for the first quarter came in quite a bit weaker than we had expected... showing a weaker and later bottom to the cycle that had been originally anticipated... Full year growth may now only come in at around 0.9 percent," said Attard Montalto.
Spiro noted that several Eastern Europe countries, like Poland, have fallen victim to the slowdown in Germany, as European stagnation creeps eastwards.
"The after-effects of the euro zone crisis are being felt throughout central Europe. Clearly the fact that Germany has been hit harder than many thought six months ago has undermined the prospects for growth, particularly in the small export-orientated open economies like Hungary, Czech Republic and Slovakia," he said.
The European Bank for Reconstruction and Development (EBRD), which invests in ex-communist countries, sharply cut its 2013 growth outlook for Eastern Europe to 2.2 percent last week, having forecast 3.1 percent growth as little as 12 weeks ago. At its annual conference, the organization cited downside risk from further deterioration in the euro zone, plus weaker activity in large regional players, such as Poland, Russia and Turkey.
Spiro said the scale and severity of the slowdown had surprised Eastern Europe's policymakers, as well as the EBRD.
"Central bankers have been caught unaware, and are falling over themselves to cut interest rates," he said. The Hungarian central bank cut interest rates for the 9th consecutive month in April, while Poland cut rates to a record low of 3.0 percent last week.
"Monthly indicators have been pointing toward a continually weak Polish economy on all fronts, while the outlook for recovery keeps getting pushed further into the future… Further rate adjustments, in addition to the 25 basis points we expect in June, cannot be ruled out as the central bank adjusts to the 'new' lower growth reality," said Kasia Zatorska, an economist at Lombard Research, in a note on Thursday.
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Analysts such as Spiro and William Jackson, an emerging markets economist at Capital Economics, said many of the region's countries have limited scope for stimulus measures because of their membership of the European Union, and its treaties regarding fiscal policies.
"I do not see a crash, because there is no prospect of a boom in Eastern and Central Europe on the economic horizon. You are looking at a couple of years at least of fairly lackluster growth," said Spiro.
—By CNBC's Katy Barnato