The scandal has embroiled Malaysian Prime Minister Najib Razak, who had set up 1MDB. Najib has consistently denied any wrongdoing
Standard Chartered Bank was slapped with a Sg$5.2 million ($3.65 million) penalty while Coutts bank was fined Sg$2.4 million for breaching anti-money laundering regulations in 1MDB-linked transactions, the Monetary Authority of Singapore (MAS) said in a statement.
The fines came after MAS, also the city-state's central bank, shut down the local branches of Swiss lenders BSI and Falcon Private Bank earlier this year for their role in facilitating illicit cross-border fund transfers involving 1MDB.
The scandal has embroiled Malaysian Prime Minister Najib Razak, who had set up 1MDB. Najib has consistently denied any wrongdoing.
An inspection of Standard Chartered Bank revealed "significant lapses" in due diligence measures, the MAS said, adding that some staff were unaware of money laundering risks.
MAS said while the breaches were "serious", its investigation "did not find pervasive control weakness or wilful misconduct" at the lender.
British bank Coutts, which in 2015 was sold to Union Bancaire Privee, was sanctioned for a lack of due diligence on customers deemed "politically exposed persons", a term for people with close government connections.
Yak Yew Chee, a former Coutts private banker who had joined BSI, was last month jailed in Singapore on fraud charges related to the multi-billion dollar scandal.
Yak was also a private banker for Malaysian financier Low Taek Jho, a close family friend of Najib who had helped the Malaysian leader set up 1MDB. Low has also denied any wrongdoing.
MAS also said it would ban former Goldman Sachs director Tim Leissner from working in the Singapore finance industry for 10 years.
Leissner, who oversaw the 1MDB account, had issued an unauthorised reference letter saying that due diligence had been carried out on Low and his family, and that no money laundering concerns had been detected.
MAS said "these statements were untrue and were made by Mr Leissner without Goldman Sachs' knowledge or consent".
Leissner resigned from the bank in February.
MAS said it would continue to work with other regulators to examine Goldman Sachs' role in 1MDB bond transactions.
"MAS has taken tough regulatory actions against various financial institutions this year for AML (anti-money laundering) control lapses," said MAS managing director Ravi Menon.
"These actions send a strong signal that we will not tolerate the abuse of Singapore?s financial system for illicit purposes."
Singapore,a regional financial hub, last year launched a probe into alleged unlawful fund flows linked to 1MDB.
Switzerland and the United States are also conducting their own investigations into 1MDB.