Authorities were alerted to the threats at around 09:10 am local time (0110 GMT) on Wednesday, the Singapore Police Force said in a statement.
It added that the threats were reported at "18 locations around Singapore, including government buildings, embassies and other places of interest".
Officers coordinated with security guards but "no items of security concern were found", it said.
The force did not disclose the specific locations involved or if any evacuations had taken place after the threats were made.
But the Ministry of Sustainability and the Environment said its office building -- which also houses the country's environment and water agencies -- had received one of the bomb threats.
"No threat items were found. Since this morning, we have stepped up security and restricted access into the Environment Building," it said in a statement on Facebook.
In its own statement, the police force said it was "aware that similar reports of email bomb threats sent seemingly by the same person, had been received by the Republic of Korea recently, which had turned out to be a hoax".
"The police take all security threats seriously and will not hesitate to take action against those who intentionally communicate false information on bomb threats," it added.
The force urged members of the public to report suspicious people and items, such as parcels with stains or wires, or those that give off a strange smell.
Anyone found guilty of "communicating false information of a harmful thing" can be imprisoned in the financial hub for up to seven years, fined up to Sg$50,000 ($37,000) or both, it said.