Under the Maintenance of Racial Harmony Bill, which was passed late on Tuesday, if an organisation is designated as a race-based entity, they will have to disclose foreign and anonymous donations, foreign affiliations and their leadership.
The government can also impose a restraining order to stop an entity from accepting donations from a foreign principal, prohibit anonymous donations or require the entity to return or dispose of donations.
The new law also empowers the home affairs minister to issue restraining orders against individuals involved in "content that prejudices the maintenance of racial harmony in Singapore".
Law and Home Affairs Minister K. Shanmugam told parliament the bill was not a panacea for all racial issues and could not prevent insensitivity or racial slights in everyday dealings.
"We acknowledge that it may be difficult to enforce offences outside of Singapore, but it signals our commitment to protect our racial harmony, even when the threat originates outside of Singapore."
The law was supported by the opposition party, even though some lawmakers urged some caution.
Opposition lawmaker Gerald Giam said the broad definition of "foreign affiliation" might unintentionally create barriers for local associations with deep historical ties to overseas groups which had helped preserve Singapore's cultural heritage.
Singapore's resident population is 74% Chinese, 13.6% Malay, and 9% Indian, with 3.3% is classified as others.
Last year, Singapore designated businessman Chan Man Ping Philip as a "politically significant person" for activities that advanced the interests of an unspecified foreign country.
A naturalised citizen of Singapore, Chan had attended the annual session of the Chinese People's Political Consultative Conference in Beijing and told local media the overseas Chinese community should form an "alliance" and "tell the China story well".
Hong Kong-born Chan was the president of the Hong Kong Singapore Business Association.