Müller told Bild that the care facility in Germany could serve 100 women and girls from Syria and Iraq.
The minister said he had spoken with five young girls on a visit to Iraq who had been captured by Isis and gang raped.
"Three of them are now pregnant. We have to take care of such girls," he said.
Müller did not provide a timetable or say where in Germany the centre would be established.
Isis launched a sweeping offensive that has overrun swathes of Iraq and Syria since June.
In November, the UN Commission of Inquiry on Syria released its first report focused on Isis crimes, presenting a horrifying picture of what life is like in areas controlled by the jihadists, including massacres, beheadings, torture, sexual enslavement and forced pregnancy.
Germany, Europe's biggest economy, has become the continent's top destination for asylum seekers. It expects around 230,000 asylum seekers in 2015, up from a predicted 200,000 this year.
The influx has spawned a far-right populist movement, Pegida, which has been staging demonstrations in cities across the country against the "Islamisation" of Germany.
Meanwhile, Germany recently announced plans to send 100 troops to Iraq to train Kurdish Peshmerga fighters to use the €70 million worth of weapons the government has sent to help fight Isis.
The news came days after Munich native Jürgen Todenhöfer, the first Western journalist to spend time in Isis territory in Iraq, came forward with details of his experience.
“Isis is a lot stronger than we think here. Its territory is bigger than Great Britain. It's supported by a vibrant enthusiasm that I've never seen in a battle zone”, Todenhöfer told TZ München about his stay in Isis-controlled Mosul.
He found fighters enthusiastic about the group's terror tactics, including beheadings live on video, which have made their advance easier as enemy forces melt away in fear.
“They say: we're doing publicly what you did secretly. You killed a lot more people in Iraq!
“Without George W. Bush's Iraq war, Isis wouldn't exist.”
Todenhöfer also commented on the group's “largest religious cleansing operation in history.”
Although people faithful to “religions of the book” – Christians and Jews – are supposed to be spared by the Muslim fundamentalist fighters, other groups such as the Yazidi are “driven out or killed” from Isis-controlled areas.
Meanwhile, “in the Arab world and everywhere else world wide, Muslims who recognize democracy are supposed to be killed. They place human laws over God's.”
For Todenhöfer, military attempts to combat Isis are futile.
“The Isis problem can't be solved militarily… if the West wanted to wipe out the 5,000 Isis fighters [who control the city], you would have to reduce Mosul to rubble and ashes.
“With every bomb that's dropped and hits a civilian, the number of terrorists is increased.”