The incendiary device was left at a golf shop in the Corn Market area at around 6.40pm.
"The device is believed to have ignited but was removed from the premises by staff and left outside," a PSNI spokesperson said.
Army bomb experts examined the device and removed it for further examination before the area was reopened after several hours.
Police have advised city centre businesses to check their premises for any suspicious objects after the latest terrorist incident linked to dissident republican activity in the city.
Anyone who was in the area at the time and who may have noticed any suspicious activity is also asked to contact detectives at Musgrave.
Nadine Afshar, manager of nearby retailer Crabtree & Evelyn, told UTV the incident had been very disruptive for the business.
"We were notified this evening to carry out security checks in the premises, a short while later the police came round and cordoned off the area," she explained.
"We were due to open to 10pm tonight but we took the decision to close because there's no passing footfall and we wanted to get the girls in the shop home safely."
She added: "We've had very big trading days that are expected and we're hopeful for, we've a lot to pull back from the damage in the city last year and we were doing that.
"We've had a really good November and December and now we're potentially going to lose everything based on the last few incidents that have happened, it's very disappointing. We're very anxious to see how the next week or so is going to pan out."
I know that there is still an absolute determination amongst traders and shoppers to continue on and not be dragged back by people behind these attacks.
Glyn Roberts, Northern Ireland Independent Retail Trade Association
Security measures have been stepped up in the city centre following a series of attacks.
On Friday evening a small explosive device hidden in a sports bag went off in the Cathedral Quarter area causing nearby restaurants and bars to be evacuated.
Last month a masked gang forced a driver to leave a bomb at the entrance to Victoria Square shopping centre car park.
The bomb partially exploded while army bomb disposal experts attempted to defuse the device.
Northern Ireland Independent Retail Trade Association (NIIRTA) Chief Executive Glyn Roberts said the latest attack was "absolutely despicable".
SDLP MLA and party Justice Spokesperson Alban Maginness said it "beggars belief that Belfast would be faced with yet another attempted act of wanton destruction".
"To place an incendiary device in a busy shopping area is both reckless and irresponsible and serves no rational purpose," he said.
"Those behind this incendiary device are anti-Belfast and just want to threaten jobs, livelihoods and people's enjoyment of our city.
"They must not be permitted to prevail. Anyone with any information, no matter how seemingly small or insignificant the detail must contact the police as a matter of urgency."
Alliance South Belfast MLA Anna Lo also condemned the incident.
"I am sickened that yet again lives have been put at risk by the mindless actions of these callous and evil individuals. There is no place in our society for those who wish to bring death, injury and destruction to our streets," she said.
"There is no support for the actions of those behind this device. We must stand together in our opposition to them. The public do not want to return to the dark days of the past.
"I would urge anybody with any information about this incendiary device to contact the police. Those responsible must be caught and brought to justice."