The detonation happened shortly before 22:00 local time (20:00 GMT) in the Schwabing district and was heard across the city, local media report.
There are reports that sparks from the explosion caused the roofs of some neighbouring buildings to catch fire.
The bomb was discovered on Monday night by building workers at the site of an old bar that was being demolished.
Overnight, 2,500 residents were evacuated from the area closest to the bomb, with others living further away being told to stay in their homes.
Experts decided it was not possible to make the device safe because of its unusual fuse, which operated by means of a chemical reaction rather than the mechanical device that many Allied World War II bombs used.
The bomb was described as a highly explosive, a 550lb (250kg) device dropped by the Americans.
It is not unusual for big, unexploded bombs to be discovered in Germany, the BBC's Stephen Evans reports.
About 600 tonnes of unexploded ordnance are discovered in Germany every year.
They are usually defused safely, though in 2010 three bomb-disposal officers were killed during an attempt to make a bomb safe, our correspondent adds.
In December 2011, the biggest bomb disposal operation in Germany since 1945 was mounted in Koblenz to defuse two bombs from World War II found in the riverbed of the Rhine.

Anthony Knockeart converted Gaetan Bong's fine cross to give Brighton the lead in an otherwise even first half.
Bournemouth loanee Murray doubled the lead from close range after the break and he tapped in his second late on.
Defeat was Forest's first of the season under new head coach Philippe Montanier, who joined in June.
Relive Brighton's win over Nottingham Forest
Adding victory to their draw at Derby on the opening day, the result saw Brighton go to the top the table ahead of the rest of the weekend's fixtures.
Murray returned to the Seagulls on a season-long loan this summer and his second-half goals made the points safe as Brighton, who finished third in the Championship last season, took control after half-time.
Tomer Hemed went close to adding further goals for the hosts, while Czech Republic winger Jiri Skalak had a goal correctly ruled out for offside.
Forest have now conceded three goals in both of the first two league games, while Brighton are yet to concede this season.

Some 3,000 people have been left homeless, according to a BBC reporter who has been to the scene.
Their houses were destroyed after mud and rocks, dislodged by the rain, plunged down the hillside.
Reports from the Democratic Republic of Congo say there have been similar problems across the border.
UN-backed Radio Okapi says 14 people have been killed on the Congolese side of Lake Tanganyika.
Burundi's President Pierre Nkurunziza has visited the scene of the landslides, 35km (20 miles) south of the capital Bujumbura.
The governor of Bujumbura district, Jacques Minani, described it as "a disaster", reports the AFP news agency.
He said that the emergency services were now searching the area for survivors.
A bomb disposal team has detonated an American bomb left over from World War II found in the German city of Munich.
[NEXT_CONCEPT]
Glenn Murray scored the first two goals of his second spell at Brighton & Hove Albion as they beat Nottingham Forest to claim a first league win of 2016-17.
[NEXT_CONCEPT]
At least 10 people are missing, feared dead, in Burundi after landslides which have destroyed hundreds of homes, officials say.