Two unattended bags gave bystanders cause for worry in separate incidents - at a bus terminal in Queen Street and at Woodlands Checkpoint - last Friday.
Chinese evening daily Lianhe Wanbao on Saturday reported witnesses as saying they were afraid the bags - a backpack and a luxury handbag - contained explosives.
Police officers were seen surrounding the suspicious-looking bags, which were later claimedby their owners.
Mr Xu Wei Lin, who was at the bus terminal on Friday, said: "The Jakarta bombing was still fresh in everybody's mind."
On Thursday, a bomb went off in Jakarta, killing eight people and injuring more than 20. Militants from the Islamic State in Iraq and Syria terrorist group have claimed responsibility for the attack.
The owner of the bag found in Queen Street was a Mr Wong.
The 50-year-old electrician told reporters he was using the bag, which contained clothes and electrical appliances, to hold a spot in the queue while he parked his electric bicycle nearby.
The Malaysian, a permanent resident in Singapore, said he has been doing the same thing - using a bag to hold his place in the queue - for a year now.
Every Friday, he takes the bus back to Johor Baru, and a connecting bus to Kuala Lumpur to visit his 80-year-old mother.
He said: "I saw the police car, but I did not realise that they were here because of my unattended bag.
"I didn't expect it to cause any misunderstanding."