The first explosion was heard early Monday in the Dinguessou neighborhood of N'Djamena, and the second came minutes later, said resident Souleymane Brahim.
"There were two explosions. The first came around 5:10 a.m. in the morning. It was followed by gunfire. The second came around 5:16 a.m.," he said.
Five police officers were among the 11 dead, said Chad's Minister of Territory and Public Security, Abderahim Bireme Hamid. He blamed extremists for the attack, saying that "the mastermind of the network was arrested yesterday."
The blasts come weeks after a double suicide bombing in the capital that killed at least 38 people and wounded more than 100 others. The June 15 attack was the first of its kind in N'Djamena and came after threats from Nigeria's Islamic extremist group Boko Haram.
There was no immediate claim of responsibility for that attack but suspicion fell on Boko Haram, the Islamic militant group based in neighboring Nigeria that has already attacked Chadian villages along the lake dividing the two countries.
Chad's prosecutor on Sunday announced that the June 15 blasts led to the arrests of 60 people from Chad, Cameroon, Mali and Nigeria. Alghassim Khamis said an active cell was identified and dismantled, leading to the seizure of "communication materials" and the arrests.
Chad has been a major military ally with Nigeria in the fight against Boko Haram, which has publicly threatened the Chadian president with retaliation.
Three days after the attack, Chad said it had launched an air assault on Boko Haram positions in Nigeria near Chad. Nigeria's government said the attacks were more likely launched in Niger.