Police searched the property in the Derrylattinee Road area of Dungannon, after a telephone warning was made to a Sinn Féin office in the Co Tyrone town on Monday morning.
"Police checked the area and nothing untoward was found," the PSNI said.
Fermanagh and South Tyrone representative Ms Gildernew said those behind the hoax would not succeed in intimidating her.
"Targeting my home, in which I have three small children, is a despicable thing to do," she said.
"Threats like this will only make me more determined to continue to represent the people of Fermanagh & South Tyrone and push ahead with my work within Sinn Féin.
"While it is worrying that someone would target my family, they will not succeed in deflecting me from my work."