It comes as senior officials from India and Pakistan plan to meet in New Delhi on February 25 to resume talks suspended in the wake of the deadly Mumbai assault, which was blamed on Pakistani-based fighters.
Dilip Band, another police official, said "the explosive was in a bag kept in the bakery" and that four foreign women were among the dead but their nationalities were not immediately known.
Indian media reported that the toll of those injured could rise.
Al Jazeera's Prerna Suri, reporting from New Delhi, said the explosion was so strong that the entire restaurant had been destroyed.
"The roof has collapsed ... Many of the injured have been shifted to various hospitals across the city," she said.
"Interestingly enough, there was an intelligence alert received by the home ministry, saying that a possible terror strike may take place on villages and crowded areas ... and various agencies had shared this information."
The authorities initially blamed the blast on an cooking-gas cylinder which exploded, but they later said they suspected it was a "terror attack".
"It's a suspected terrorist attack ... because it appears the bomb blast arose from an unattended package which was left behind in the bakery," GK Pillai, India's interior secretary, told Al Jazeera.
"The whole country has been put on high alert. A team from the CBI [Central Bureau of Investigation] will be shortly on its way from Delhi to assist the Mumbai police team in the investigation of this blast."
The Press Trust of India news agency quoted an unnamed official source as saying the blast was caused by an improvised explosive device.
Maharashtra police said an investigation was under way to establish the cause of the explosion.
The site of the Pune blast was close to Chabad House, a Jewish cultural and religious centre run by the orthodox Chabad-Lubavitch movement whose members were targeted in the Mumbai attacks.
Pune is about 100km southeast of Mumbai, India's commercial capital.