The 17-year-old suspect, who is believed to be Syrian, although his nationality has not been confirmed by the police, was arrested yesterday in the Uckermark region in Brandenburg, north-east of Berlin.
In the message, the teenager said "he had joined the jihad," the Islamist war, police said, adding that "evidence of the planning of a concrete act has not yet been identified during the police investigation".
According to the state's interior minister, Karl-Heinz Schroter he had sent a message to his to his mother and written his intentions about the plot.
He entered Germany in 2015 and sought asylum, police said.
He has been living since 2016 in a home for minor refugees in Uckermark. The home he was living in is now being searched by the state criminal investigation office.
The suspect was to be questioned further on Wednesday, and was being kept in detention until then.
German security officials have been warning for some time about global terrorism groups as the country remains on alert.
Twelve people were killed in a Berlin terrorist attack last December, when police say a Tunisian man drove a truck into a crowded Christmas market.
The Islamic State has claimed responsibility for attacks in Germany in the past year, including the murder of a teen in Hamburg, a suicide bombing in Ansbach and an axe rampage on a train in Wuerzberg that injured five.