Al-Masri says he was released in Albania in May 2004, and that his captors told him he was seized in a case of mistaken identity.
Condoleezza Rice, the US secretary of state, and other US officials have declined to address the case.
But Angela Merkel, the German chancellor, said the US had acknowledged making a mistake with al-Masri.
Al-Masri said he was pursuing the petition because, four years after the incident, no government has recognised his ordeal.
"I just want the German government to acknowledge what happened to me," he said.
Prosecutors in Munich issued warrants for the arrest of 13 suspected CIA agents at the end of January 2007, accusing the unidentified suspects of wrongfully imprisoning al-Masri and causing him serious bodily harm.
Eva Schmierer, a ministry spokeswoman, said: "The German justice ministry then spoke to the US justice department about the Munich warrants and was told that extraditing the agents would jeopardize 'American national interests'".
After receiving that answer, the ministry decided not to pursue the warrants further, Schmierer said on Monday.
The new case seeks to force the government to reconsider extradition for the agents.
The ministry confirmed that it had received the petition, but said it had no immediate comment.
Human-rights campaigners have seized on al-Masri's story to press the US to stop flying terrorism suspects to countries other than the US where they could face abuse, a practice known as "extraordinary rendition".
In other legal action in the case, civil-rights attorneys from Albania and Macedonia said they have filed freedom of information requests in both countries seeking documents related to al-Masri's case.
They are also pursuing a criminal case against CIA officers involved in al-Masri's alleged abduction in Macedonia.
Darian Pavli, an attorney who filed the information request in Albania and joined the German attorneys at a news conference on Monday, said the process there and in Macedonia could culminate in a case before the European court of human rights.
Meanwhile, attorneys from the American Civil Liberties Union (ACLU) have taken legal action on al-Masri's behalf in the US.
Ben Wizner, an ACLU attorney who filed an unsuccessful complaint in 2005 against former CIA director George Tenet and the CIA officers involved in the case, said that the Aclu filed a new petition in April through the Inter-American Commission on Human Rights, a body that seeks to establish international laws.
Wizner said that the new petition accuses the US of failing to respect al-Masri's basic human rights.
"These are all little pin pricks," Wizner said. "It's all about trying to narrow the space in which the CIA can engage in systematic human rights violations."