After entering a shop, the man caught fire when his device appeared to go off prematurely, Sky News reported. He fled the store — Golf Madness in the city's Comarket area — furiously trying to beat out the flames.
"We believe this man may require treatment for burn injuries, to neck, face and hands," Sky News quoted Chief Supt. Alan McCrum of the city's police department as saying. The man escaped.
On Friday night, a bomb exploded close to a busy restaurant in the city as police were clearing people from the area, leaving no one hurt, the Police Service of Northern Ireland said.
The explosion took place just before 7 p.m. local time in the city's Cathedral Quarter, which was filled with Christmas shoppers and people enjoying an evening out.
Police said the device "could have killed or maimed anyone nearby," and about 1,000 people were affected by the evacuation and cordoning off the area.
Police gave no immediate indication of who could have been behind the attack.
Northern Ireland endured decades of so-called "troubles" when armed groups seeking unification with the Republic of Ireland and rival groups determined to keep Northern Ireland within the United Kingdom both waged violent campaigns.
The troubles largely came to an end with the Good Friday Agreement signed in 1998, but Northern Ireland is still plagued by occasional outbreaks of sectarian unrest and attacks by small dissident groups that have not accepted the peace deal.