A 1.5 metre by one metre (five feet by three feet) chunk from an unidentified object was found Wednesday morning in the grounds of a warehouse on the outskirts of the western city of Poznan, police said.
Police later said a second similar-sized object had been located several hours afterwards in a forest a few kilometres from where the first was discovered.
No casualties or damage were reported.
The Polish Space Agency (POLSA) said a stage of the Falcon 9 R/B rocket made "an uncontrolled re-entry into the atmosphere" at about 0346 GMT.
It said the rocket was part of a Space X Starlink Group launch from Vandenberg Air Force Base in California on February 1.
The launch was to put Starlink satellites into a low-level orbit.
The debris left spectacular luminous trails visible in the sky in western Poland, witnesses said.
POLSA spokeswoman Agnieszka Gapys said the agency was speaking with SpaceX, which is controlled by Elon Musk, the world's richest man, PAP news agency reported.
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