The small explosion happened shortly before 7pm on Friday in the Exchange Street West area.
Police were at the scene near St Anne's Cathedral, one of Belfast's busiest nightlife spots, following a telephoned warning.
Around 1,000 people were evacuated from restaurants and other premises, including a hotel, The MAC, the cathedral and apartments, on one of the busiest nights in the run-up to Christmas.
No-one was injured, but police say passers-by could have been killed or injured.
They said the warning, which was received about an hour earlier by the Irish News, gave the wrong location for the bomb.
The PSNI says the device "was left at a different location to that named in a call to a newspaper".
"That call warned of a device at a hotel in the Cathedral Quarter, but it was actually left on the footpath adjacent to the front of a busy restaurant," a statement said.
Those who carried out this attack have nothing to offer except disruption and destruction.
Alan McCrum, PSNI
Police confirmed the area was being cleared when the device exploded.
They later issued a warning to shopkeepers and businesses in the wake of the attack in the city centre.
"Police in Belfast are asking shopkeepers and business people to check their premises thoroughly before closing tonight," a spokesman said on Friday night.
"The exact nature of tonight's explosive device in the Cathedral area has not yet been established."
Chief Superintendent Alan McCrum said: "This was an attack on the people of Belfast going about their normal lives on a busy night for socialising in the city. This attack ruined the night out for these people."
Earlier Belfast woman Geraldine Corry told UTV of her shock as "this thing exploded right in front of my eyes".
"I had a fair idea it was definitely a bomb," Ms Corry told UTV's Sharon O'Neill.
"The police said that I was extremely lucky because I was still in my apartment and at the window at the time."
"It's just shocking, absolutely shocking."
Had it fully exploded or had it been a larger device then I might not be standing here. The front of the apartment would have taken the full blast which is where I was standing at the time.
Geraldine Corry, eyewitness
The finger of suspicion is now pointing at dissident republicans, days after senior officers warned they could strike again in the city.
Justice Minister David Ford said: "Yet again we see a reckless attempt to kill and injure innocent people in Belfast."
"The people carrying out these attacks have set out no reason and explained no cause for their acts of senseless violence.
"Their only aim seems to be to injure and disrupt," the Alliance leader added.
NI Secretary of State Theresa Villiers says the attack aimed at "a busy entertainment area of the city" shows that "these terrorists are stooping to a new low".
"Tonight's bomb attack on Belfast City Centre and on the people of Belfast is absolutely deplorable," she said.
"After tonight's attack, I would reinforce the importance of working with the PSNI and reporting any suspicious activities, no matter how small."
This small minority want to drain the economic life from Belfast - but we will not let them succeed.
Theresa Villiers, Secretary of State
DUP Lagan Valley MLA Jonathan Craig said: "It was a miracle that no one was injured as the bomb exploded."
The Policing Board member said: "No family wants such tragedy visited on them at any time of the year but certainly not at Christmas."
North Belfast Sinn Féin MLA Gerry Kelly said the explosion was "an attack on all the people of Belfast and those that had come into the city centre to shop or enjoy the build-up to the festive holidays".
"Thankfully no one was hurt."
Paul McErlean, from the Cathedral Quarter Trust, said the area had "grown to become Belfast's social and cultural epicentre".
"It will not be dragged into the past by the indefensible actions of this faceless minority."
The Belfast Chamber of Trade & Commerce and Pubs of Ulster also strongly condemned the latest in a series of terrorist incidents in the city.
They ignore the strength of public support for normality and peace, especially at this Christmas season.
David Ford, Justice Minister
Last month a 130lb proxy car bomb partially exploded at the entrance of the underground car park of the Victoria Square shopping centre as army bomb experts attempted to defuse it, prompting police to step up security measures against dissident republican activity in the city in the run-up to Christmas.
Earlier this month, two separate police patrols came under fire in north Belfast and west Belfast - no-one was hurt but the attacks are being treated as attempted murder.
On Friday night, SDLP MLA and Justice Spokesperson Alban Maginness said: "It is a matter of grave concern that such an incident could take place, that even given heightened security that a bomb could be placed in this area."
"The anti-democratic gang behind this bomb must not be allowed to prevail," he said.
"Anyone with any information, however small, must contact the police as a matter of urgency."
An emergency centre was set up at City Hall for evacuated residents.
C/Supt McCrum said: "Police would appeal for continued community support and vigilance on the run-up to Christmas in seeking to disrupt or deter any further attack on the city."