The first blast occurred outside an Imambargah (Shia prayer hall) in Abbas Town at about 7 pm as people were leaving after prayers. The second explosion went off in the same area within 10 minutes, witnesses said.
The explosions caused extensive damage to residential buildings and destroyed several shops in the area, senior police officials said.
The injured and deceased included women and children.
Many victims were trapped under the rubble as teams worked to rescue them.
"Initial investigations show the first blast was of low intensity and planted in a motorcycle and the second one was of high intensity which went off in a car," Deputy Superintendent of Police (DSP) Qamar Ahmed said.
A police officer, Usman Arian, said the blasts had completely destroyed some blocks of a residential apartment close to the site, dozens of shops and two banks.
Seemi Jamali, a doctor at the state-owned Jinnah hospital, confirmed that they have recorded 10 deaths and were treating around 40 injured.
Another doctor at the Patel hospital, which is located close to Abul Isphani road, confirmed that they had received eight bodies and four more people succumbed to injuries in hospital.
The explosions occurred at a time when the Prime Minister, high-profile political leaders and top officials were present in the city to attend the engagement ceremony of Sharmila Farooqi, an advisor to the Sindh Chief Minister.
Television channels reported that due to heavy security provided for the engagement ceremony at Mohatta Palace, senior officials of the police and para-military rangers didn't reach the blast sites even after the lapse of two hours.
"This incident shows the apathy of this government. At a time when so much destruction and deaths have been caused.
Hundreds of families are in mourning... this ceremony continues," senior political analyst Kamran Khan said.
Meanwhile, an official of the Edhi welfare trust whose rescue workers and ambulances were busy carrying out rescue operations at the affected sites said bodies were also taken to the Abbasi shaheed and other private hospitals.
"The damage caused by the blasts is very high. Two blocks of apartment buildings, Iqra towers and Rabia flower city collapsed after the blasts while the condition of other blocks which were damaged by the blasts are also in bad shape and could collapse," Kazim Reza said.
He said that the third and fourth floors of one apartment block had caught fire after the blasts and rescue workers and fire workers were trying to control the situation.
"Some bodies have also been recovered from the rubbles of the collapsed blocks. There could be more people killed or trapped inside the debris," he added.
Ehteshamuddin, the chief fire officer of the city, said firefighters faced problems reaching the blocks because of the damage around the affected areas.
The Mutthaida Qaumi Movement and other Shia bodies have announced a complete strike in Karachi to protest the blasts while the private schools association, transporters bodies and the all Karachi trade body have announced a complete shutdown on Monday.