The cool, rainy weather is expected to continue until the end of the month, with the cloudy skies clearing up in February - just in time for Chinese New Year.
There will be "a few rainy episodes" this month, but these are conditions typical of the north- east monsoon, said the Meteorological Service Singapore (MSS).
Total rainfall for the month is expected to be about 242mm, the long-term average for January.
February is usually one of the driest months of the year, with a long-term average monthly rainfall of 161mm.
The cooler temperatures and windy conditions of the past week were due to the effects of a north-east monsoon surge, said an MSS spokesman.
Between last Dec 26 and 29, the daily minimum temperature ranged from 23.6 to 24 deg C. The long-term mean daily temperature for December is 23.5 deg C.
"This is a surge of cold air from northern China that results in a steady strengthening of north- easterly winds over the South China Sea," the MSS spokesman explained.
The north-east monsoon typically lasts from late November to January, causing between two and four monsoon surges. These are periods of occasionally windy conditions, cooler temperatures and prolonged and widespread moderate to heavy rain lasting between two and five days.
In November, the north-east monsoon brought heavy thundery showers that resulted in flash floods in several parts of Singapore, including Kovan and Tampines Road.
Intense rain caused water from a canal to overflow into residential areas, trapping parked cars, causing power shutdowns and flooding homes.
Meanwhile, it has been very windy in many parts of Singapore in the past week, with the daily maximum wind speed across the island ranging from 19.6 kmh to 23.6 kmh.
"This was stronger than the average daily maximum wind speed of 18.3kmh for this month," the MSS said.
The strong wind and cooler temperatures have had some Singaporeans feeling the chill, especially at night.
"Sometimes the wind is so cold I open the windows only a small gap, and still use a blanket," said civil servant Choy Tze Wei, 25, who lives in a 14th-floor, four-room flat in Potong Pasir.
The MSS said windy conditions are expected to ease over the next few days with the weakening of the monsoon surge.
Said Ms Choy: "That's a pity, I was just beginning to get used to it."