The device ignited at a shop in the Corn Market, the latest attack on the city's shops, bars and cafe area, before it was removed member of staff and left outside.
It comes after a bomb exploded in the nearby Cathedral Quarter on Friday evening, which was busy with people enjoying Christmas nights out.
Dissident republicans have stepped up the number of terror attacks in the days before Christmas in an effort to cripple the festive trade.
Nationalist SDLP Stormont MLA Alban Maginness said: "It beggars belief that after the placing of a bomb in the Cathedral Quarter on Friday night 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.
"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."
A Police Service of Northern Ireland (PSNI) spokesman said the Cornmarket area was closed following the latest discovery at 6.40pm. He said the area was been sealed off to allow Army experts examine the device.
He added: "Police are advising city centre businesses to check their premises for any suspicious objects."
Corn Market is a shopping focal point from the site of a blast on Friday night when Christmas party goers were forced to evacuate busy bars and restaurants. A sports bag with a small explosive inside ignited on the pavement in the city's Cathedral Quarter.