The guards found their exhausted mother on Thursday clutching a fourth child - a two-year-old son - near the border.
They had been trying to enter Poland illegally. They had spent four days in the cold and wet, the woman said.
The bodies were found 1,100m (3,600 ft) up a mountain in the Bieszczady range. The girls were aged six, 10 and 13.
Thousands have fled Chechnya in more than a decade of conflict.
The mother and surviving child are now in hospital.