The politician was informed that the threat was linked to any attempt to go to her constituency office or continue to live at her East Belfast home.
Loyalists protests have been held outside her constituency office after an Alliance motion to stop flying the Union flag at Belfast City Hall all year round was passed earlier this week.
Ms Long said she was alerted about the threat by the PSNI in the early hours of Friday.
"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," she said.
"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."
Alliance properties have been targeted during flag protests across Northern Ireland this week.
Around 150 people held a peaceful demonstration outside the Lisburn office of Alliance MLA Trevor Lunn on Friday afternoon.
They attached large Union flags to the railings opposite the building.
In Carrickfergus the constituency office of Stewart Dickson MLA was burnt out on Wednesday during serious disorder which followed a large protest.
A 29-year-old man, who was arrested following a search in the Minorca Drive area of the town by police investigating the attack, has been released on bail pending further inquiries. Items were recovered for examination.
Two teenagers - a 17-year-old girl and a 15-year-old boy - have been charged with affray and unlawful assembly.
Also that night, Michael and Christine Bower had the front window of their home broken by a paint bomb in Bangor, and the office of Dr Stephen Farry was attacked.
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.
Naomi Long MP
It comes after a vote was passed over the flag policy at City Hall.
Nationalists wanted to remove the flag altogether but Alliance, which holds the balance of power, put forward a compromise which meant the Union flag flies on designated days.
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."
First Minister Peter Robinson condemned those responsible for the threat.
The DUP leader said: "Such threats are an affront to democracy and an attack on us all.
"As someone who in the past has been visited many times by the police to be told of death threats issued against me, I know how difficult and testing a time this is.
"My thoughts and prayers are very much with Naomi at this time and I would call upon all concerned not to allow themselves be used by those who have very sinister motives. Regardless of political difference, public representatives should not be attacked or threatened in anyway."
Deputy First Minister Martin McGuinness called for the threat to be withdrawn immediately.
"This is the work of fascists who cannot accept the democratic decision of Belfast City Council," he said.
"Threats remain against Alliance Councillor Laura McNamee, Sinn Féin's Gerry Kelly and Cllr Jim McVeigh. Each and every one of these threats must be lifted."
SDLP Foyle MP Mark Durkan said he wanted to show his "support and solidarity" for Ms Long.
"These vicious tactics which we have seen against a number of Alliance Party representatives this week have to be condemned without excusery of any kind," he said.
"Democratic parties need to be together in unequivocally repudiating threats and attacks from any quarter or against any party."
Meanwhile, a UUP spokesperson said: "We again place on record our condemnation of all forms of violence including threats of violence made most recently to the East Belfast MP Naomi Long and other elected representatives."
Police say there are aware of a number of protests ongoing on Friday evening in Greater Belfast and Bangor. The areas, where traffic disruption could be experienced, include Lanark Way and Finaghy crossroads.
An earlier protest at Shaws Bridge has ended.