Finance minister Heng Swee Keat announced the move in his 2016 budget announcement.
Under the scheme, approved trustee companies are granted a lower tax rate on income from providing certain trustee and custodian services, and trust management or administration services.
The scope of activities for trustees to qualify will now align with the FSI scheme, which will mean that a broader range of activities is now covered.
The concessionary tax rate will now rise from 10% to 12%, Heng said.
Singapore-based tax expert Valerie Wu said: "It is heartening that they are extending this tax incentive scheme in the first place, and in fact expanding the scope of qualifying activities. This signals the continuing recognition of the importance of the wealth management and trust industry."
The tax incentive scheme was due to expire on 31 March. MAS will release further details of the change by June 2016.
Singapore's corporate income tax rebate is also to be increased from 30% to 50% under the budget.
Heng said that the move is designed to help smaller businesses. The rebate will be capped at S$20,000 ($14,600) a year for 2016 and 2017.
This is the first time since 2001 that Singapore has given a 50% rebate, Heng said.
The rebate will cost the government an extra S$180 million ($131 million) over the two years, bringing the total support given to companies under the rebate to close to a billion dollars over two years, he said.
The budget announcement also included an increase to the personal income tax cap, to S$80,000. This will only affect the highest earners, it said, and "99% of tax-resident individuals will not be affected".
"This cap will make our personal income tax system more progressive. Nevertheless, our personal income tax burden remains low. Our personal income tax structure must allow us to continue to stay competitive," Heng said.
The personal income tax relief cap will take effect from 2018 and is expected to raise an additional $100 million a year, he said.