He will now take over managing rivals Helsingborg, it was announced later.
Tabloid Aftonbladet broke the news early Monday and it was later confirmed by the club in a press statement.
"Henrik Larsson has informed us that he will not be extending his contract. We would have liked him to continue but we obviously respect his decision," said Falkenberg sports director Håkan Nilsson, who added that Larsson's decision had not come as a surprise.
Helsingborg is Larsson's former home club, where he started as a player before being transferred to bigger clubs abroad, such as Celtic and Barcelona. He also played his last four seasons as a player for the club.
Lars Lagerback, who once successfully managed the Swedish national side, told SVT at the weekend that the 43-year-old Larsson is good enough to be a possible future replacement for Erik Hamrén as Swedish national coach.