The women – who are aged 89 and 92 – were attacked at their home in the townland of Feddyglass, Raphoe, at 5pm yesterday.
One of them had to be taken to hospital after suffering a suspected broken hip and was later treated for shock.
Inspector Goretti Sheridan appealed for information on the incident, saying a UK-registered Ford Focus was seen acting suspiciously in the area at the time.
She appealed for anyone with information to call detectives immediately on 074 91 67100.
“This was a particularly nasty aggravated burglary and we would ask anyone with information to come forward as soon as possible,” she said.
Telephone lines were cut and the women locked inside the house when the thieves left. They had been thrown to the floor and threatened during the incident.
They made off with personal possessions and cash.