Local news reports said the killings in Cuautepec Barrio Alto appeared to have stemmed from a dispute over drug sales.
Among those slain were a 13-year-old girl and a 15-year-old boy, according to a source with the prosecutor's office.
The adult victims were a man and three women, the source said, adding some were members of the same family.
No suspects have been detained in the killings, and details were sketchy.
The drug violence that for years has afflicted parts of northern Mexico surfaced in the capital in May 2013 when 13 youths were abducted from a Mexico City bar.
Their bodies were found in August in a common grave.