The source said that the body of the woman was found in the bathroom of a flat on eastern Moscow's Prospekt Budennogo.
"During a search of the flat, officers also found a cellophane bag containing the head of the victim. Forensic reports suggested the woman's death came about as the result of blows to the head and body with a heavy object about three days ago," the source said.
Officers suspect the killer intended to cut the body up into parts with a saw before disposing of it. However, they were unable to suggest what might have stopped the suspect from doing so.
The woman's 50-year-old son has not been seen since the presumed date of the murder.
The beheading is the second to have taken place in Moscow in the last few days.
On Saturday, in northern Moscow, the headless body of a 26-year-old woman was thrown out of a window.
"The incident happened at about 10 p.m. [19:00 GMT]," a police source told the Life.ru news website.
"A blood-covered corpse fell at the feet of a group of passersby. After recovering from the shock, they called the police," he said.
Police arrested a 36-year-old Muscovite in connection with the murder. Although he was reported to be in a state of extreme alcoholic intoxication, he managed to tell police the victim was a 26-year-old woman, one Yelana T from the West Siberian city of Surgut.
The incidents come just over a week after the decapitated body and severed head of an Asian man were discovered in southern Moscow.
