It follows a decision by the US Federal Aviation Administration and two Japanese airlines to ground all of their 787s after a sixth problem with the aircraft in less than two weeks.
The planes will be grounded until the risk of possible battery fires is addressed, a US official said.
The federal agency plans to work with Boeing on a plan to allow the Dreamliners to "resume operations as quickly and safely as possible".
The EASA typically implements safety directives when they are issued by the country where the aircraft was originally designed - in this case the US.
Poland's state-controlled LOT Airlines said it would seek compensation from Boeing.
It expects delivery of three more Dreamliners by end-March, but would only take them if the technical issues have been resolved,
deputy chief Tomasz Balcerzak told a news conference.
Ethiopian Airlines and Qatar Airways have also decided to ground their Dreamliner aircraft.
Qatar Airways' CEO Akbar al Baker said: "In light of recent events surrounding the Boeing 787 Dreamliner worldwide, we are actively working with Boeing and the regulators to restore full customer confidence in the 787.
"Qatar Airways will resume 787 operations when we are clear that the aircraft meets the full requirements of the Airworthiness Directive and our standards which assure the safety of our passengers and crew at all times. So we are not flying the aircraft until and only such a time this is achieved."
Ethiopian Airlines said it had not encountered any problems and is hoping to return the planes to service as soon as possible.
United Airlines is the only American carrier to have 787s and has six of the aircraft in its fleet.
The decision comes just days after the FAA Administrator Michael Huerta and Transport Secretary Ray LaHood declared the plane safe.
All Nippon Airlines (ANA) announced it was grounding all 17 of its 787s after one was forced to make an emergency landing in west Japan on Wednesday.
Japan Air Lines Co Ltd (JAL) said it would also suspend all Dreamliner flights scheduled to leave Japan on Wednesday over safety concerns.
Public broadcaster NHK said the ANA aircraft landed in Takamatsu and all passengers on board were evacuated after smoke was seen in the cabin.
ANA spokeswoman Naoko Yamamoto said: "It made an emergency landing at Takamatsu because there was an error message during the flight.
"It is true that the aircraft has recently seen a series of troubles. But we cannot say if this has something in common with previous problems."
A statement later said a battery problem had forced the emergency landing.
TV footage showed emergency chutes deployed from the plane at the airport, on Japan's fourth largest island of Shikoku.
ANA said 129 passengers and eight crew were on board. Some of the passengers were reported to have suffered minor injuries as the plane was evacuated.
The aircraft was travelling to Haneda Airport in Tokyo.
On Friday, oil was discovered leaking from another ANA operated Dreamliner at Miyazaki airport in southern Japan.
On the same day, a cracked cockpit window was also discovered on another of its 787s.
Last Wednesday, a domestic flight was halted by ANA because brake parts to the rear left undercarriage needed replacing.
And a JAL jet was also grounded at Boston Logan International airport in the US following an engine fuel leak.
Another JAL 787 filled with smoke shortly after passengers and crew had disembarked last Monday.
Japanese authorities announced on Monday they would investigate the fuel leak.
Japan is the biggest market so far for the Dreamliner, with ANA and Japan Airlines Co flying 24 of the 50 Dreamliners delivered to date.
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