A petrol bomb was thrown at the front window of the house in Wallace Park on Sunday and the flames were put out by a passer-by.
Later on Sunday, a bullet was pushed through another family's letterbox.
That incident - on a Protestant family - is also being treated as sectarian. A brick was also thrown at their house.
Rasharkin is a religiously mixed village, though with a Catholic majority.
In the last six months, there have been 18 sectarian attacks in the village.
It is understood to be the second time in three weeks that Mrs Baird's home has been attacked.
Daithi McKay of Sinn Fein described the incident as a case of 'attempted murder'.
"It is quite clear they are being targeted because they are a Catholic family," he said.
"The family are not involved in anything political. People are shocked and very angry that they have been singled out."
Baird has captained Northern Ireland in the past, and was first given the role against Liechtenstein in August 2007.
The 28-year-old, who signed a new deal at Fulham last week, arrived from Southampton in July 2007 and was a key part of the Cottagers' team that reached the Europa League final in May.
Baird started his career at Ballymena United before joining Southampton's youth academy in 1998 and made his first team debut in March 2003.
He joined Fulham for £3 million, being signed by former Northern Ireland boss Lawrie Sanchez.
By Saad Noor
