The explosion at the restaurant, on North Main Road, happened at about 1900 (1330 GMT), when it was packed with diners.
"It appears that an unattended package was noticed in the bakery by one of the waiters who apparently attempted to open the package when the blast took place," Indian Home Secretary GK Pillai was quoted as saying by the Associated Press news agency.
"We heard a big noise and we all rushed out. The impact was so great that there were body parts everywhere," Vinod Dhale, who works at the restaurant, told Reuters.
Anti-terror squad officers have gone to the scene.
AT THE SCENE
Prachi Pinglay BBC News, Pune
The German Bakery, on the ground floor of a corner building in a plush area of Pune, has been reduced to rubble.
The rest of the building is still intact and anti-terrorist squads from Mumbai have gone in to try to determine the type of explosive used in the blast.
The street has been cordoned off and the area is very quiet now.
Whenever I have visited this bakery in the past - last time was a few months ago - it has always been very crowded.
It was a very quaint, old place, the limited seating areas full of students and foreign visitors from the nearby Osho Ashram eating Western food.
A security alert was issued for Chabad House, a Jewish centre for learning in the vicinity of the German Bakery, in October 2009, India's Home Office said.
But the German Bakery was not deemed to be at risk at the time.
Nearby shops were badly damaged and reported to have been splattered with blood.
"I came running to the bakery after hearing the explosion. I found people lying all over the place", local resident Abba More told AP.
Initial reports had suggested the explosion was caused by a gas cylinder.
The German Bakery is near the Osho Ashram, a mystic centre popular with visitors to Pune.
The Chabad centre, run by the Jewish Orthodox Chabad-Lubavitch movement, is also in the vicinity.
Members of the Chabad-Lubavitch were targeted in the 2008 Mumbai attacks, and in October 2009 the home ministry issued a security alert for the Chabad centre in Pune.
No-one has yet said they carried out the latest attack.
However Home Minister P Chidambaram described it as "a significant terrorist incident".
"All the evidence points to a deliberate plot," he told AFP.
The bomb blast comes a day after India and Pakistan agreed to meet for talks in Delhi on February 25.
The talks will be their first formal negotiations since the Mumbai attacks.
No conclusions could be drawn yet as to who was responsible for the blast, Mr Pillai said.
"Forensic investigations have just begun. Till they are completed, we will not know who is [involved]", he told AP.
The home ministry has issued an advisory to all state governments to be on high alert.
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