The father of the family, which also included two women and five children, is currently in custody, police said on Wednesday.
The family reportedly moved house seven times in a short period in the district of Vulkaneifel in the small western town of Daun.
Several property owners have pressed charges against the family for fraud, though police are working on the assumption that many more have been defrauded since 2009.
The family, which changed its name with each move, also lived in Schleswig-Holstein, Saxony-Anhalt, Hesse, Bavaria, and North Rhine-Westphalia.
Heinz-Peter Thiel, Daun police director, said the father of the family had called himself “Dr. Abdul” on several occasions and was able to put down deposits with “thick wads of cash.” But then the entire family would suddenly disappear without cancelling its rental agreements.
State prosecutors have begun an investigation.