The 45-year-old man, whose nationality was not given, was previously known to police, said authorities in Rüdesheim on the Rhine river in the central state of Hesse.
The woman, who had previously separated from her husband, was taken to hospital by helicopter, police said.
Two other people were injured in the fire in the shelter that houses 14 people.
Germany took in around one million asylum seekers last year and expects about 300,000 arrivals this year.
The mass influx has forced Germany to accommodate the newcomers in hostels, sports halls and army barracks, where crowded conditions have at times sparked violent clashes.
In June, two men were investigated for starting a massive fire at a large refugee home in Düsseldorf after a fight broke out over meal times during the Muslim holy month of Ramadan.