The man and women were detained on Thursday in Ecatepec, a crime-ridden northeastern suburb of the capital, prosecutors in Mexico state said in a statement.
After searching two buildings, investigators found additional human remains in buckets filled with cement, and wrapped in plastic in a refrigerator, the statement added.
A judge ordered the couple to remain in detention as the investigation proceeds.
Forensics experts are attempting to identify the victims.
Hundreds of people vented their outrage in the streets of Ecatepec on Sunday.
Carrying candles and white flowers, they demanded justice and an end to rampant femicide in Mexico state.
"Not one more! Enough is enough!" said their placards.
Mexico has suffered for years from waves of violence against women and girls.
More than 90 per cent of crimes go unpunished in the country.
According to UN Women, seven women and girls are killed in Mexico every day.
The local non-governmental organisation Semaforo Delictivo recorded 188 killings of women in the country between January and March this year -- an 18 per cent increase from the same period last year.
In past years, Ciudad Juarez, on the border with the United States, was a focal point for the killings and disappearances of women, but Ecatepec too has become an epicenter of the violence.
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