Tan was arrested on Thursday, a day after the incident at the mosque.
Police said previously that a suspicious parcel containing pork was found at the location. It prompted evacuations and the deployment of hazardous materials specialists from the Singapore Civil Defence Force.
One person was assessed for breathlessness and taken to Sengkang General Hospital, SCDF said on Wednesday.
Police said preliminary investigations showed that the accused was allegedly involved in several similar cases at other mosques around Singapore.
Visiting Al-Istiqamah Mosque on Wednesday night, Acting Minister-in-charge of Muslim Affairs Muhammad Faishal Ibrahim told the media that he was alerted to the incident earlier in the evening and said that “such incidents are unacceptable”.