Several shots smashed through the window and hit a 23-year-old man lying in bed at that time, Hessian police said in a statement. It added the refugee was "lightly wounded." He has now been discharged from hospital.
Criminal police cordoned off the area around the asylum center at Gleisstrasse. There are currently no suspects and the cause of the attack is still unclear, police said.
Dreieich is housing around 300 refugees, local media estimate. Germany is one of the EU’s main destinations for thousands of migrants fleeing hostilities in the Middle East and Africa. This has led to tensions in the country, including attacks on centers accommodating refugees.