Prosecutors also said one of the three explosives used in Tuesday evening’s attack contained metal strips.
Two letters claiming responsibility for the attack were being investigated, they said.
Prosecutors are treating the blasts as a terror attack but say the precise motive is unclear at present.
A spokeswoman for Germany’s federal state prosecutor in Karlsruhe, Frauke Koehler, said: “Two suspects from the Islamist spectrum have become the focus of our investigation. Both of their apartments were searched, and one of the two has been detained.”
Koehler said three letters containing the same text found near the site of the blasts indicated that the attacker had links to so-called Islamic State.
She said: “Among other things they demand the withdrawal of [German] tornado fighter jets from Syria and, I quote, the closure of Rammstein airbase.”
That letter is being analysed to see if it is authentic.
Another letter was published online, in which left-wing extremist groups claimed to have carried out the attack, but the state prosecutor had reason to believe this letter was not authentic.
