The man was arrested last month on suspicion of planning an militant attack in Germany.
In 2015 militants stormed the Bardo museum and killed 21 foreign tourists.
"I can confirm that the talks between us and the Tunisian side have been successful. The terrorist is sitting in custody and I expect that he will soon be deported," de Maiziere told broadcaster ARD for the Bericht aus Berlin programme.
The Tunisian, identified by German media as Haikel S., was arrested last month and is believed to have recruited for Islamic State here, German prosecutors have said.
Germany raids apartments of four Turkish imams suspected of spying
He had lived in Germany for a decade until 2013 before re-entering the country to seek asylum in August 2015, five months after the storming of the Bardo museum, the prosecutors said.
Tunisian investigators suspect the Tunisian asylum seeker was involved in the assault and had issued a warrant for his arrest in June 2016.
Earlier Italy said it had expelled a Tunisian who might have had links with the man who killed 12 people in Berlin by driving a truck into a Christmas market.
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