The explosion happened on Thursday when people were preparing a pre-dawn meal on the first day of the Muslim holy month of Ramadan in a residential area of Karachi, the capital of Sindh province, local police chief Rizwan Patel said.
Rescuers were still removing rubble to search for any survivors trapped under the debris, he said.
The death toll was initially reported at 13 but Patel said it rose to 16 after three more bodies were pulled out from the rubble.
Pakistan's President Asif Ali Zardari expressed sorrow and condolences to the victims' families and directed authorities to ensure the best possible treatment for the injured.
He also called for a swift completion of rescue operations and urged the Sindh provincial government to enforce building codes, check gas cylinder safety and conduct a thorough inquiry to help prevent similar incidents.
Most houses and apartment buildings in Karachi, like elsewhere in Pakistan, are supplied with natural gas for cooking.
However, many households also rely on liquefied petroleum gas cylinders because of low natural gas pressure.
In July, a gas explosion following a wedding reception at a home in Pakistan's capital, Islamabad, killed eight people, including the bride and groom.
The blast occurred as guests had gathered to celebrate the couple, authorities said.
