Fiji head coach Cotter quits seven months before Rugby World Cup
The 61-year-old took charge of Fiji in 2020 after coaching French clubs Clermont Auvergne and Montpellier.
He also took Scotland to the 2015 World Cup quarter-finals.
Tevita Tuiloa, the union's interim chief executive, refused to be drawn on who could replace Cotter - "it could be a Fijian or from abroad" - but expects to name a coach by the end of February.
"Fiji Rugby was blessed to have Vern Cotter come on board, but the call (to resign) came directly from him due to personal reasons," Tuiloa told a press conference in Suva.
"Time is against us to find a coach to take the Flying Fijians to the next level (at the World Cup), but we are confident we have the players."
Fiji have been drawn with Australia and Wales - both of whom also changed head coaches recently - as well as Georgia and Portugal in Pool C at the Rugby World Cup, which will take place in France and starts on September 8th.
Fiji's best performance was at the 2007 tournament in France, where they reached the quarter-finals after a win over Wales, before losing to eventual winners South Africa.