Judge Rosi Datzmann ordered the Brazilian player, who had been on bail pending the outcome of the case, to be taken immediately into custody.
Breno's house, in the leafy Munich suburb of Gruenwald, burned down last September while he was recovering from injury. His family was out at the time.
The talented Breno joined Bayern as an 18-year-old four years ago and had high hopes of becoming their defensive anchor.
He failed, however, to earn a starting spot and having also been plagued by injuries was released by the club last June.
Bayern Munich said they had heard the news with regret.
"Our hope was that Breno could have continued his footballing career and his life together with his family," Bayern said in a statement.
Prosecutors had argued that Breno, who was under the influence of alcohol at the time, used several lighters and possibly some fire accelerant and lit objects around the house.
They had asked for a five-year sentence.
Breno's lawyer, Werner Leitner, said that there were still doubts about whether arson was the cause of the fire.
"He has nothing but family and football," he said. "Give Breno a chance."
Local media reported that Breno was likely to spend two-and-a-half-years in a German prison before being deported.
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