Isabel Martinez, 33, has been charged with five counts of malice murder, five counts of murder and six counts of aggravated assault.
Police found the bodies after responding to a 911 call in Loganville, located outside of Atlanta.
Another child inside the home was taken to hospital with serious injuries.
Gwinnett County police Cpl Michele Pihera said: "Right now we believe we have everybody involved in this crime.
"What her motivations are for committing this horrendous crime, we still don't know."
The suspect called police from the property at 04:47 local time (08:47 GMT) to report a stabbing.
Cpl Pihera said the mother spoke Spanish in the 911 call, which initially made it difficult for operators to communicate with her.
The county sheriff's office said US Immigration and Customs Enforcement were getting involved in the case, but did not specify further details.
In Chicago, relatives of the family said Ms Martinez had been "a little down and depressed" because her father died in Mexico one day after Father's Day.
Police said the children were all under the age of 10 and the man in his mid-30s.
A knife appeared to be used in the attack, but a medical examiner will determine how each of the victims died, Cpl Pihera added.
A neighbour told WSB-TV that the woman may have been home with her deceased family members for hours before police arrived.
"It's reasonable to believe they were in the home all night," Gwinnett police Corporal Deon Washington told the Atlanta Journal Constitution.
A Georgia mother is in custody after her four young children and their father were found dead in an apparent stabbing at their home, police said.