"As far as I know, Turkish authorities as early as last year knew the fact that the man who bombed the US embassy in Ankara entered Turkey illegally," Hans-Peter Friedrich told reporters during a visit to Istanbul.
Cooperation between Turkey and Germany was "working well", he added.
The visiting minister's remarks came after Turkish Prime Minister Recep Tayyip Erdogan on Monday accused European countries, particularly Germany and France, of letting "terrorists" roam freely across Europe.
German media reported that the leftwing militant who blew himself up outside the United States embassy on Friday went to live in Germany after his release from a Turkish prison in 2001.
According to a Süddeutsche Zeitung report, the bomber had sought political asylum in Germany but his request was turned down and he was asked to leave the country for his connection to the extremist Revolutionary People's Liberation Front (DHKP-C).
He was not put under surveillance as he was not thought to pose a threat, the paper added.
The DHKP-C has claimed responsibility for the US embassy attack that killed a Turkish security guard.
Erdogan said some European countries were not heeding Turkey's calls for solidarity in its fight against terrorism.
"I must openly say that we have not received needed support from some European countries... despite so much pain and losses," he said in remarks carried by Turkey's Anatolia news agency. "We no longer have tolerance for this carelessness and this neglect."
The DHKP-C, a fiercely anti-US group with Marxist roots, is blacklisted by Washington and the European Union as a terrorist organisation and has carried out several attacks in Turkey since 1970s.
The attacker, identified as Alisan Sanli, was previously jailed in Turkey for his involvement in an attack on an Istanbul military compound in 1997.
Turkish police have detained three people for providing him with false documents to enter Turkey but they were later released, Anatolia news agency reported.