The MAS estimates about 5-10 percent of borrowers have a total debt-servicing burden of over 60 percent of their income, with that potentially rising to 10-15 percent of households if mortgage rates rise by 300bps.
Song noted that banks' charge-off rate for credit cards at the end of December was at 5 percent, up from 4.8 percent at the end of 2012 and 4.3 percent at the end of 2011.
"It tells a story to a certain extent," he said. "The amount written off by banks is still modest, but nonetheless, the trend is there," Song noted.
(Read more: Higher wealth taxes on the cards for Singapore?)
Others aren't terribly concerned by the rising number of bankruptcies.
"I do not think the number of bankruptcies poses a systemic risk to the economy," said Daniel Wilson, an economist at ANZ, via email.
But he added, "most households have borrowed more during this abnormal period of very low interest rates. This is one of the key reasons why we view rising interest rates as a risk for the medium term outlook in Singapore. Rising interest rates coupled with a softening property market is not the best combination."
Changing cultural values may also be driving some of the increase in bankruptcy orders. Traditionally for Asian families, declaring bankruptcy would be considered a "loss of face" and would be avoided.
"It's less taboo nowadays, certainly it's much more the case than say a decade ago," Song said. "With people encouraged to be entrepreneurs, there's less of a stigma to be declared bankrupt."
A stronger entrepreneurial spirit does appear to be driving some of the increase in bankruptcy orders.
While "traditional" problems – such as people living beyond their means and racking up debt on credit cards and auto loans – drive many bankruptcies, entrepreneurship gone wrong is spurring more filings, said R Nandakumar, an attorney who does insolvency work for both companies and individuals at RHTLaw Taylor Wessing LLP. .
"The bank will normally require personal guarantees from the director (of a company) for financing," Nandakumar said. "If the company fails, then the directors become liable."
(Read more: Singapore dollar still draws safe haven seekers)
While the percentage increase in the number of bankruptcy orders is shocking, one factor likely to help keep the absolute number low – and debtors negotiating directly with their creditors – is that filing for bankruptcy in Singapore is far from the relatively painless process in many Western countries.
"It's not an easy process. Going through the bankruptcy regime in Singapore is actually difficult," Nandakumar said.
Not only will bankrupts need to transfer assets to an official assignee and make payments for three to five years, but they could be disqualified from being officers at companies and will need to apply for permission for any trips outside the country, Nandakumar noted.
Indeed, with those high hurdles that come with bankruptcy, Nandakumar believes the rise in bankruptcy orders may have less to do with economic travails and more related to the city-state's population increase – around 5.4 million people lived in the city-state at the end of 2013, up from 4.0 million in 2000.
—By CNBC's Leslie Shaffer. Follow her on Twitter