It was informed about the "racially motivated" damage on the King Street building on Sunday morning.
A spokeswoman for Polish Social and Cultural Association said graffiti was found on the front entrance at about 06:00 BST and had been washed off.
The centre's chairwoman said staff were "very disturbed" by the find.
Metropolitan Police said: "Shortly before 11:00 police were informed of an incident of alleged racially motivated criminal damage to a building in King Street, W6.
"Officers from Hammersmith and Fulham borough attended and enquiries are ongoing."
Joanna Mludzinska, chairwoman of Polish Social and Cultural Association (POSK), said: "We were very disturbed and upset this morning to find really unpleasant graffiti all over the building when the staff came in."
Andy Slaughter, the Labour MP for Hammersmith, said on Twitter: "This is an outrageous act that disgusts not only me and the Polish community but everyone in Hammersmith & Fulham.
"We are proud in west London to be the centre for the Polish community in the UK and the home of posklondon.
"Posklondon was founded by the generation who fought with Britain against Nazism and who helped build our inclusivity and prosperity," he added.
"Racist" graffiti was found scrawled on a Polish cultural centre building in Hammersmith, west London, the Met Police said.