The uncertainty around the smallest nation by population ever to qualify for a men's World Cup comes less than five weeks before a testing opening game against Germany in Houston.
Rutten took the job in February after the 78-year-old Advocaat stepped down citing his daughter's health issues.
Under Rutten, the team lost two warm-up games in March — against Australia and China, both in Australia — with players reportedly wanting Advocaat back.
"I regret how things unfolded but I wish everyone the best," Rutten said in a statement posted by the Curaçao soccer federation. He previously coached Dutch clubs Twente, PSV Eindhoven and Feyenoord, and Schalke in Germany.
The federation is expected to hold a news conference on Tuesday.
Curacao are joined by Ghana, Morocco and Saudi Arabia in changing coaches since the World Cup draw in December.
Curacao is an autonomous territory of about 156,000 people in the Caribbean within the Netherlands kingdom. The team relies almost entirely on players born and raised in the Netherlands.
The team also will play Ecuador in Kansas City and Ivory Coast in Philadelphia.
Advocaat took his native Netherlands to the quarter-finals in 1994, and coached South Korea at the 2006 edition.
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