Athens sports daily newspaper SportDay said Bjärsmyr became the first active player in the club’s history to seek legal action for unpaid wages.
The move was made by his Martin Dahlin, who on behalf of his client is claiming €870,000 ($1.05 million).
Bjärsmyr signed a four-year contract in July 2009 worth €1.6 million.
The 26-year-old has hardly featured this season as the team locked up second place in the Super League behind champions Olympiakos.
Panathinaikos have deep financial problems and an emergency shareholders meeting is scheduled for next Wednesday to seek a way out of a reported €27 million debt.
Founded in 1908, Panathinaikos are one of the oldest and most successful teams in Greek football history, having won 20 Greek championships and 17 Greek cups. They reached the final of the European Cup in 1971.
While the club has continued to enjoy success in recent years, financial problems have forced them to offload a number of key players.
Bjärsmyr signed for the team in 2009 after moving to southern Europe from IFK Gothenburg. He has played three times for the full national team.