The person spoke on the condition of anonymity Thursday because the Canadiens have not announced the move.
The abrupt move comes four months after Montreal signed the 39-year-old Streit to a one-year, $700,000 contract after he won a Stanley Cup with Pittsburgh last season.
They made the move to restock a depleted group of defenseman. Andrei Markov left to play in his native Russia, Alexei Emelin was claimed in the NHL expansion draft and Nathan Beaulieu was traded to Buffalo.
Streit had no points in playing just two of Montreal's first four games.
This is Streit's second stint with Montreal after spending his first three NHL seasons with the Canadiens. He's topped 40 points in six of 11 seasons and overall has 96 goals and 338 assists in 786 games.