The party said Naomi Long was advised to leave her home on Thursday night and not to go to her constituency office on Friday.
Sinn Fein's Jim McVeigh, councillor on Belfast City Council, confirmed that he has also received a death threat.
Ms Long said: "I recognise that there are strong feelings about the issue of flags, on both sides; however, in a democracy these arguments have to be made in a peaceful way. I refuse to allow this threat to stop me from delivering the valuable constituency service which I have developed since first elected in 2001, a service to all of the people of east Belfast.
"This is not an attack on an individual or on a party, but a wanton attack on the democratic process. It is long past time that this vicious campaign of intimidation and violence was brought to a permanent end."
Elected representatives from the non-sectarian Alliance Party have borne the brunt of loyalist anger since Belfast City Council voted on Monday to restrict the number of days the Union flag is flown over City Hall.
A constituency office belonging to East Antrim MLA Stewart Dickson was set alight during rioting in Carrickfergus and two councillors in Bangor, Co Down, escaped injury when their home was hit with paint bombs.
Belfast councillor Laura McNamee, who spoke out during the debate on Monday was also told not to return home in the east of the city after threats were posted on social media.
Ms Long added: ""In the run-up to the vote on Monday there was a concerted effort on the part of the DUP and UUP, with the delivery of thousands of leaflets in predominantly unionist areas, not only to whip up tensions with inflammatory language and bogus claims about the Alliance Party's position, but to focus that anger on me personally, even though I am not a councillor or directly involved in the decision-making process.
"It is little wonder that, in that context, those who would resort to violence would also target me in this way. There is a particular responsibility on those who stoked the fire and fanned the flames of this situation to reflect on the consequences of their campaign and learn the lessons of this entire sorry episode."