The man and his wife, whose nationality was not released, were detained late Tuesday night after officers raided their flat and came across “unknown substances” that are now being analysed by specialists, Cologne police said in a statement.
“We decided to take very swift action to ward off possible danger,” police spokesman Andre Fassbender told DPA news agency.
The 29-year-old Tunisian man is suspected of “handling toxic substances”, police said.
It was not immediately clear if his wife was still in custody on Wednesday.
According to German broadcaster NTV the woman is a German national who recently converted to Islam. She was said to be pregnant.
In a sign of how seriously authorities are taking the case, federal prosecutors have taken over the investigation.
According to DPA, investigators will now be probing whether the suspects were planning an attack.
Police officers, including special forces, were still combing the couple's flat on the first floor of a large apartment building on Wednesday morning.
Chemical experts wearing protective were seen removing plastic bags from the scene.
The couple's children have been taken into the care of city authorities.
Germany remains on high alert for jihadist attacks after several assaults claimed by the Islamic State group in the country in recent years.
In the worst such attack to date, Tunisian asylum seeker Anis Amri rammed a truck into crowds at a Berlin Christmas market in December 2016, killing 12.