The board says the photo was posted on Facebook and staff have now cleaned up the Komagata Maru memorial in Harbour Green Park at Coal Harbour.
It says police are investigating the incident.
Park board chair Sarah Blyth says members are saddened and deeply offended by the disgraceful act.
In May 1914, the charter ship with 376 people from India arrived in Vancouver's harbour, but immigration officials refused to allow the passengers to disembark.
The ship stayed anchored in the harbour for two months before returning to Calcutta, where a riot erupted and 20 people died.
"The monument was created in partnership with the Khalsa Diwan Society to embrace multiculturalism and remind people about the devastating impact that racial intolerance and discrimination have had upon our community," said Blyth in a statement.
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