The men, aged between 19 and 46, were arrested at several locations in nearby Batam island on Friday.
The plot allegedly involved firing a rocket from Batam, just south of Singapore, at Marina Bay - an upmarket, waterfront area.
Singapore officials said they were aware of the plot and security had been stepped up.
Indonesian police spokesman Boy Rafli told BBC Indonesian that the suspects were now being questioned. It is not clear whether the men had the ability to carry out such an attack.
Police said they were investigating whether the suspects had links to Indonesian militant Bahrun Naim, one of the alleged masterminds of the 2016 Jakarta attacks.
Singapore's Marina Bay is one of the country's most popular tourist destinations and the Marina Bay Sands hotel is an iconic structure on Singapore's skyline.
"What we understand so far is that they were planning to attack vital objects, busy areas including police offices," police spokesman Agus Rianto told Reuters news agency.
Singapore's Ministry of Home Affairs (MHA) said in a statement: "Our security agencies have been coordinating closely with the Indonesian authorities since the discovery of this attack plot, to monitor the activities of the group and to apprehend those involved."
Indonesian police have arrested six people they say were planning to attack Singapore.