In an online statement on Monday, police in the city's Bao'an district said a 30-year-old unemployed man was detained as a suspect. Jiang is a migrant worker originally from Chongqing.
The family posted a notice inquiring about Jiang's whereabouts in September 2015 after he lost contact.
Shenzhen police said that Jiang had answered questions with a clear mind and that they were investigating the crime as well as Jiang's mental state.
Sunday's killings were the latest in a series of knife attacks in the country. In January, Just in January, a man stabbed 11 students to death at a kindergarten in Guangxi province.
Firearms are largely unobtainable for ordinary Chinese, and such attacks are more often carried out with knives or homemade explosives.