"Those coming from a country exempted from visa requirements would then register online and say who they are and what they want in the EU," the minister told Chemnitz-based Freie Presse regional paper on Friday.
Friedrich added that Germany was a popular "destination for criminals and terrorists." An online register of "personal data," he said, would "make it more difficult to come to Germany undiscovered." This could also include biometric data such as fingerprints or photos, he suggested.
At the same time, the minister wanted to clarify that travel should be made easier for business travellers from more countries, in reference to requests by Russia and Turkey for exemption from EU visa requirements for their citizens.
"A relaxation or even a complete exemption from visa requirements is associated with a loss of control that must be compensated in some other way - for example with the kind of immigration system that the US has in place," Friedrich told the paper.
Travellers to the US who do not require a visa, for example those from EU countries, must register their passport details and the purpose of their visit online with Department of Homeland Security before travelling.
A similar system could be set up in the EU, said Friedrich: "Only under these circumstances could there be moves to relax some of the visa requirements."
Open borders in Europe are good for all citizens, he added, but "we need a greater awareness of the fact that we need to secure our borders."