"Traces of contamination have been discovered at two places in the flat where [Kovtun's] former wife lived," a police statement said.
Radioactivity was later detected at the home of the ex-wife's mother in the town of Haselau, west of Hamburg, police said.
Police said they were questioning Kovtun's ex-wife, an unnamed 31-year-old.
Police experts are trying to determine if the radioactivity came from polonium 210, the highly radioactive substance which killed Litvinenko.
"His [Litvinenko's] murder has to be condemned because he was murdered for his views and his knowledge."
Mikey, London, UK
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British authorities are treating Litvinenko's death as murder.
Following the discovery of the radiation traces at the two properties in Germany, the investigation was widened to include a Germanwings airliner used by Kovtun on November 1 - the day he flew to London to meet Litvinenko.
No radioactivity was detected and the aircraft was returned to service.
Kovtun, one of three Russians who met Litvinenko in London on November 1, was also reported on Friday to be suffering from radiation sickness.
There have been conflicting reports on Kovtun's condition, with a lawyer denying claims that he had fallen into a coma.