The Monetary Authority of Singapore (MAS), the country's central bank, said it also imposed lifetime bans on two bankers and a 15-year prohibition order on a third following a two-year review of lenders involved in 1MDB-related transactions.
The Swiss giant was fined Sg$700,000 ($505,000) and United Overseas Bank was penalized Sg$900,000 for breaching anti-money laundering laws and for control lapses related to fund flows involving 1MDB, the MAS said in a statement.
"These include weaknesses in conducting due diligence on customers and inadequate scrutiny of customers' transactions and activities," the statement said, adding however that MAS did not detect "pervasive control weaknesses within" the two banks.
MAS also directed the banks "to appoint independent parties to assess and confirm... that rectification measures have been effectively implemented" and punish errant staff.
Allegations that huge sums were misappropriated from 1MDB triggered a scandal in Malaysia that has embroiled Prime Minister Najib Razak, though he has denied any wrongdoing.
Singapore, a regional financial centre known for its tough stance against corruption, launched a probe following allegations that its financial system was used to move illicit funds.
Four private bankers have been jailed so far as Singapore became the first country to hand down criminal convictions related to the 1MDB investigations.
The United States and Switzerland have also launched their own probes.
Two bankers, including Swiss national Jens Fred Sturzenegger, were slapped with lifetime bans from doing business in Singapore's financial industry and a third was banned for 15 years, the central bank said.
MAS added it intends to issue bans on three other people. Previously, MAS banned a former Goldman Sachs banker from working in the city-state's financial industry for ten years.
MAS said its review of financial institutions involved in 1MDB-related flows "is the most extensive it has ever taken".
"The review uncovered a complex web of transactions involving numerous shell companies and individuals operating in multiple jurisdictions, including the United States, Switzerland, Hong Kong, Luxembourg and Malaysia," it added.
Singapore has also closed the local branches of two Swiss private banks -- BSI and Falcon Private Bank -- used in the transfer of illicit funds.
"Our financial industry is in a better position today than it was when the abuses stemming from the 1MDB-related flows took place," MAS managing director Ravi Menon said.
"The price for keeping our financial centre clean as it grows in size and inter-connectedness is unstinting vigilance."