The woman left her home in Berlin on March 21 and was reported missing by her husband soon afterwards.
Mikhalchuk, 52, also known as Anna Alchuk, had lived in Berlin since November 2007 with her husband Mikhail Ryklin, a philosophy professor at Berlin's Humboldt University. Mikhalchuk also taught at the university.
"We will be able to say for sure that the woman found dead is Anna Mikhalchuk only after a DNA test on the weekend. But going by a number of signs, including the wedding ring, the husband identified his missing wife," the officer told RIA Novosti.
Mikhalchuk was searched for by divers and several dozen police officers with sniffer dogs, but was not found until last Thursday. The body was discovered in the Spree River near in Berlin's central Mitte district.
In Russia, Mikhalchuk was charged with inciting religious hatred after taking part in a controversial art exhibition focusing on religion in 2003, but was acquitted in 2005.
German police said that although Mikhalchuk had reported receiving death threats, nothing so far had prompted them to believe that her disappearance was linked to her life or activities in Russia.
The police officer also said there were no traces of violence on her body and the case was an apparent suicide.
Mikhalchuk's husband contacted police late last Friday, saying that his wife had left home at about 3:30 p.m. and had failed to return by midnight. Ryklin said his wife had gone shopping, although most shops were closed on that day, Good Friday.
Much of the artwork displayed at the 2003 Moscow exhibition entitled 'Caution, Religion! was vandalized during the show. These included a painting of Jesus Christ's face imposed on a Coca-Cola logo next to the words "This is My Blood".
The vandals were charged with hooliganism, but cleared after the Orthodox Church and several members of parliament stepped in, angering human right activists and triggering complaints that freedom of expression was being restricted in Russia.
