Most of those infected were foreign construction workers, and all lived or worked within the same region of the country, said the health ministry.
None were known to have travelled to Zika-affected areas recently. Thirty-four people have fully recovered but seven are still in hospital.
Zika generally has mild effects but has been linked to severe birth defects.
It is suspected of causing a condition called microcephaly, a deformation in which babies are born with small heads.
Zika, which is spread by mosquitoes but can also be sexually transmitted, was declared a global public health emergency by the World Health Organization in February.
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Singapore declared its first imported Zika case in May, a 48-year-old local who had travelled to Brazil, where the outbreak started.
On Saturday, it announced that a 37-year-old Malaysian woman had contracted the virus locally. She is the only confirmed female case so far.
Thirty-six of the 41 cases announced on Sunday were foreign workers who worked in the same construction site.
Work at the site has been halted after housekeeping was found to be "unsatisfactory with potential breeding habitats favourable to mosquito breeding".
The ministry said in a statement that it could not "rule out further community transmission, since more of those tested positive also live or work in other parts of Singapore".
"We expect to identify more positive cases," it added.

The government in Havana says those to be freed include inmates due for conditional release next year, as well as a number of foreign prisoners.
Those found guilty of crimes against state security will not be eligible, seemingly ruling out several high-profile political prisoners.
The Pope will make a three-day visit to the island next week.
According to Cuba's state-run newspaper Granma, prisoners were chosen for early release depending on the severity of their crimes, amount of time served, and good behaviour.
Among those to be freed are a number of inmates over 60, prisoners under 20 years old with no prior criminal records and inmates with chronic health conditions.
No prisoners with sentences for murder, other violent crimes or drug trafficking will be released, the paper said.
Pope Francis is expected to meet with Fidel Castro if the former Cuban leader's health allows.
The 78-year-old Argentine pontiff is credited with helping bring about last December's diplomatic thaw after the decades-old enmity between communist Cuba and the US.
He was directly involved in organising a series of secret diplomatic meetings between the two sides.
The Roman Catholic Church has maintained relations with Havana since the revolution and Pope Francis himself is no stranger to Cuba. He was there during Pope Benedict XVI's visit in 2012 and is the author of a book on Cuba.
Singapore has confirmed 41 cases of the Zika virus which were locally transmitted.
[NEXT_CONCEPT]
Cuba has said it will release more than 3,500 prisoners in a goodwill gesture ahead of a visit by Pope Francis.