An Iraqi man was found dead on Friday in a van used to smuggle a group of about 30 people into Germany.
The 32-year-old had been dead for “several hours” when police found the vehicle outside the town of Schoepstal in Saxony, near the border with Poland, police said.
About 30 people were also found crammed into the van.
The driver, said to be a 42-year-old man, ran off and police were in pursuit. The driver of a second vehicle suspected of helping the operation, a 48-year-old man of Turkish origin, was arrested.
Authorities in Germany have registered an increase in people entering illegally from Poland in recent weeks, mostly coming via Belarus.
Many of those picked up by police are Iraqis and Syrians who flew to Belarus and then crossed into Poland before travelling west to Germany in the hope of claiming asylum there.
The EU has accused Belarusian President Alexander Lukashenko of flying migrants from the Middle East and Africa to Minsk and then sending them into the bloc on foot in retaliation for sanctions imposed over a crackdown on the country's opposition.
In October alone, 4,890 migrants entered Germany from Poland via Belarus, German authorities said. To date, about 7,300 have entered the country.
A slowdown in arrivals is “currently not in sight”, a police spokesman said on Friday.
To cope with the influx, Germany has tightened border controls with Poland, with Interior Minister Horst Seehofer sending 800 extra police officers to the area.
On Wednesday, Mr Seehofer said more than 1,000 migrants had entered in a single day this week for the first time in many years.
“If you extrapolate that to a month, then you can see that there is an urgent need for action,” he told Bild TV.
Last Saturday, a suspected smuggler was taken into custody after 31 migrants from Iraq were found in a van near the Polish border.
The influx of migrants has provided fuel for Germany's extreme right, with police last week breaking up a rally of about 50 armed activists who had gathered to oppose migrants trying to cross the border.