A leaked email suggests Defence Minister Christine Lambrecht was told to keep the plan secret.
She went public only days later with the offer to send two of the US-made launchers to Poland.
“Defence Minister Lambrecht is turning into a security risk for Germany,” said opposition MP Thomas Rachel.
The plan came after two stray missiles landed on Polish territory on November 15, killing two people.
An incorrect claim that Russia had fired the missiles briefly threatened to escalate the war in Ukraine.
Germany responded by offering two Patriot launchers to defend the skies of eastern Poland.
In an email seen by German newspaper Bild am Sonntag, Poland replied on Friday, November 18 that it was studying the proposal.
An official at the Polish Defence Ministry reportedly added: “At the same time we want to ask and recommend that you refrain from publishing information.”
But only two days later, Ms Lambrecht told a German newspaper about the plan to deploy two launchers.
Nato member Poland initially said it was accepting the offer and suggested placing the launchers on the border with Ukraine.
But Warsaw has since changed tack and suggested the Patriots should be given directly to Ukraine, leaving the fate of the launchers uncertain.
“The missile flew through Polish territory in a few seconds,” said Deputy Prime Minister Mariusz Blaszczak. "This is not nearly enough time to effectively strike it down."
In response, Germany said the Patriots should stay on Nato territory as part of the alliance’s integrated air defence.
The plan envisaged in Berlin was that the launchers would be operated by German personnel, meaning it would not be in Poland’s gift to donate them to Ukraine.
Germany said it had separately been supplying Ukraine with IRIS-T air defence systems since mid-October.