Germans are "riled up" and "full of fear", Horst Seehofer told a press conference, after four violent attacks in Germany in less than a week.
In the latest, on Sunday, a Syrian immigrant detonated a bomb, killing himself and injuring 15 people.
A gun attack in Munich was the deadliest - with nine people killed.
What is going on in Germany?
Ansbach attacker: From asylum seeker to IS suicide bomber
What drives individuals to commit mass killings?
Mr Seehofer said that Germany must "do whatever is necessary to protect our citizens".
He said: "What we have here is an entirely new dimension of terrorism, the Islamist-minded terrorism, and we have to have intense discussions on this challenge in Bavaria and in Germany as well as prevent and repress it.
"That is the big challenge we face, and therefore any attempts to contextualise the problem are inappropriate.
"Every attack, every act of terrorism is one too many. Islamic terrorism has arrived in Germany and the people are rightly expecting us to stand up to this courageously."
The recent spate of attacks began on a train in Wuerzburg in Bavaria on 18 July. Five people were wounded by an axe-wielding teenager from Afghanistan who had pledged allegiance to so-called Islamic State.
Last Friday, nine people were killed by a teenage gunman in Munich. He then shot himself dead in an incident that was not believed to be jihadist-inspired.
Sunday's bomb attack was also in Bavaria, in the town of Ansbach.
The Ansbach bomber had been rejected for asylum in 2015.
Germany has been the main destination of Syrian asylum seekers entering the EU, most of them arriving irregularly in Greece via Turkey.
Bavarian Interior Minister Joachim Herrmann on Tuesday gave more details of the attack.
The attacker, identified as Mohammad D, had enough materials to make a second bomb.
Mr Herrmann questioned how the man had been able to assemble a bomb while living in a state-funded shelter for asylum-seekers.
He called for legal thresholds for deporting failed asylum-seekers to be lowered.
Germans shaken by violence
German media on the attacks
WATCH: 'We must fight hate with love'
The prime minister of Bavaria has urged the German government to address public concerns about security and immigration after a spate of terror attacks.