Jens Fred Sturzenegger, 42, who headed the Singapore branch of Swiss lender Falcon Private Bank, was also fined Sg$128,000 ($89,000) after he pleaded guilty at a district court.
Allegations that huge sums were misappropriated from 1MDB have triggered a scandal which has embroiled Malaysian Prime Minister Najib Razak, though the leader has denied any wrongdoing.
Singapore, a regional financial hub known for its transparency and tough stance on corruption, last year kicked out Falcon Bank and another Swiss Bank BSI for what regulators called massive lapses in financial controls.
Swiss banks were allegedly used to transfer illicit funds.
The United States and Switzerland have also launched investigations into the fund but only Singapore has meted out convictions so far.
Sturzenegger was initially slapped with 16 charges, including six for allegedly failing to report suspicious transactions totalling $1.7 billion in March 2013.
Another ten charges were for giving false information to Singapore authorities who were investigating the use of the city-state's banking system as a conduit for the transfer of illicit funds involving 1MDB.
He pleaded guilty to three charges of money laundering and three charges of giving false information. The other charges were taken into consideration in the sentencing.
Three Singaporean private bankers from BSI have already been jailed in relation to the scandal.
Among them was Yeo Jiawei, who was sentenced to 30 months in prison for witness tampering and obstructing the 1MDB probe.
It was revealed during Yeo's trial that he worked closely with Malaysian financier Low Taek Jho, also known as Jho Low, a family friend of Najib.
Najib founded the 1MDB fund while Low helped set it up and played a key role in its decisions. Low has also denied wrongdoing.