Troopers discovered that a substance believed to be "some type of oil" was splashed or poured on the granite memorial, located at the beginning of the causeway that heads out to Castle Island.
Rep. Stephen Lynch posted on Twitter he was "deeply hurt and disgusted by the hateful attack" on the memorial.
"It's saddening that these men who gave their very lives, very lives for freedom and democracy and fighting against Nazi oppression that their memories would be defamed in this way," Lynch told Boston 25 News.
More than 200 names are etched into the granite blocks, which now have oil seeped into them.
Officials spent the day using soap to scrub and also power-washing the memorial but said that additional work needs to be done.
Anyone with information about who may be responsible for the vandalism is urged to call the state police's South Boston office at 617-740-7710.