The independent report, commissioned in the wake of the Black Lives Matter movement, found that employees of color often felt excluded and ignored by white colleagues at the ministry.
It said that while employees were "not usually abused in person", they often experienced "verbal aggression" by hearing others disparage people on the grounds of skin color, religion or origin.
"A number of employees have said that people have been referred to as 'monkeys', 'bokitos', 'negroes' and 'Black Pete' because of their skin color," the report said.
"African countries have been described by one employee as 'monkey countries.'"
Black Pete, or Zwarte Piet, is a blackface festive character in the Netherlands and Belgium who traditionally accompanies Saint Nicholas, while Bokito was a gorilla who went on a rampage from Rotterdam zoo in 2007.
Dutch Foreign Minister Wopke Hoekstra said the report was "painful and confrontational".
"What a number of colleagues in the department and missions worldwide have experienced is unacceptable and this touches me deeply," he tweeted.
The independent report involved interviews with 33 people and focus groups including a total of 47 people, including "bi-cultural" foreign ministry employees working in the Netherlands and abroad, embassy staff and some white employees, it said.
It found that many of those questioned believed they were "ignored and passed over", with locally hired embassy staff in particular feeling excluded.
The report said that the findings had "raised the question of whether there is institutional racism. We conclude that this is the case."
The Netherlands has long promoted its image as a liberal and multicultural society, but the country has in recent years been reckoning with its history as a colonial and slave-trading power.
Reported plans for the government formally apologize for slavery later in December have been mired in confusion, with groups from former colonies saying they have not been consulted and calling for it to be postponed.