The Lagan Valley representative is the second MP from Northern Ireland to have his life threatened in the past week.
Mr Donaldson was informed by police that his life and the lives of his wife and children were at risk on Tuesday.
He said: "Police this morning received a serious threat to the effect that myself, my wife and children and my colleague Edwin Poots, his wife and children would be shot and the police are treating this threat very seriously."
Mr Donaldson said he was appalled by the threat.
"Whatever they may think of my politics as a unionist and someone who is proud to be British, it is beyond belief that people would target my wife and children in this way," he said.
I won't be intimidated by these threats, just as I have not been intimidated by such threats in the past but this is the first time my family has been threatened in this way.
Jeffrey Donaldson, DUP Lagan Valley MP
Mr Donaldson said he had consistently condemned threats against elected representatives in the past.
"Regardless of where these threats may have emanated from, this is an assault on democracy itself and when people resort to violence or threat of violence against democratically elected politicians then we really have gotten to a very low ebb," he added.
Mr Poots, who serves as Health Minister in the Northern Ireland Executive and is an MLA for Lagan Valley, says dissident republicans are behind the threats.
"It is not something that is new to them but it is something we will resist," he said.
Both Mr Donaldson and Mr Poots have voiced their strong opposition after the flying of the Union Flag was restricted at Belfast City Hall last week.
East Belfast MP Naomi Long was also threatened after the Alliance amendment reducing the number of days the Union Flag flies over City Hall was passed.
Earlier on Tuesday, First Minister Peter Robinson revealed two senior DUP members had been informed of the danger by police.
"Many of our members have been under death threat for a very long period of time so we take it seriously and we empathise with anybody who is under threat," the DUP leader told UTV.
Mr Robinson also condemned the latest loyalist street violence, branding those who are behind the trouble the "enemies of the people".
"This is terrorism. This is a despicable act on the part of those involved and they have no right to call themselves loyalists and be attacking the forces of the state," Mr Robinson told UTV.
The threats against Jeffrey Donaldson, Edwin Poots and their families are wrong and should be withdrawn immediately.
Martin McGuinness, Deputy First Minister
Deputy First Minister Martin McGuinness said all threats against democratically elected representatives should be withdrawn immediately.
"There is no justification for this type of intimidation from any grouping or organisation.
"These are the latest in a series of threats against elected representatives since the beginning of the loyalist protests against the decision of Belfast City Council over a week ago.
"Threats remain against other representatives. Each and everyone of these need to be lifted immediately."
Alliance leader David Ford said he extended "support and solidarity of the Alliance Party" to the DUP members.
"Any threat to a political representative is an attack on democracy. The threats, intimidation and attacks that we have seen against members of my party as well as those of the DUP and Sinn Féin must stop now."
Speaking in the House of Commons on Tuesday before news of the latest threats emerged, Northern Ireland Secretary of State Theresa Villiers told MPs: "The right of elected representatives to go about their daily business without the threat or fear of intimidation is one of the hallmarks of our democracy.
"And the actions of those who carry out such threats are nothing less than an attack on democracy."