Police said the viable bomb was discovered after officers investigating dissident republican activity stopped a car in Londonderry - the UK's City of Culture for 2013.
Witnesses said police rammed the vehicle in the Westway area of Creggan at about 8.40pm yesterday.
The army bomb disposal unit was called in after officers became suspicious about contents in the car.
A spokeswoman for the Police Service of Northern Ireland (PSNI) said: "Detectives from the serious crime branch investigating ongoing dissident republican activity in the Londonderry area arrested four males in the Creggan area of the city last night.
"At approximately 8.40pm, police stopped a car and subsequently arrested two males aged 47 and a male aged 40 after the discovery of what is believed to be a viable IED (improvised explosive device). A fourth male aged 41 was arrested nearby."
All four suspects were taken to the PSNI serious crime suite in Antrim for further questioning. The spokeswoman added: "They are assisting police with their inquiries."
It is understood the men who have been arrested are well-known dissident republicans from the Co Londonderry area.
The discovery of the bomb comes ahead of a visit by US secretary of state Mrs Clinton, who is due to meet Northern Ireland's First and Deputy First Ministers at Stormont this morning.
Mrs Clinton's husband, former US president Bill, was a key player in the peace process during the 1990s.
SDLP Foyle MLA Pat Ramsey said people were angry at the disruption caused by this latest bomb alert.
He said: "Once again, the people of the Creggan are the victims of disruption, distress and anger. People are genuinely fed-up with this.
"People are first of all looking forward to Christmas with their families and then, next year, to the City of Culture. And this may have something to do with it because the dissidents have consistently said we will not have anything resembling normality during the UK City of Culture year.
"It was freezing cold last night and there were people in their 80s and 90s who were moved from their home. Some forgot medication.
"The people they tell us they represent are the people who are being disrupted. This has to stop.
"Thank God the police found the bomb and the people of this city or somewhere else are not waking up to destruction today."
Dissident republicans who were behind the murder of prison officer David Black last month have been particularly active in the Londonderry area in recent years.
They are opposed to the UK City of Culture status that has been bestowed on the city for next year. Attempts have been made to blow up the City of Culture offices on a number of occasions because it is seen as a highly symbolic target.
In March, dissidents tried to bomb Derry Courthouse and there have been attacks on police stations in the city. They have also been responsible for a number of murders and have forced young men to leave Derry.
Tensions in Northern Ireland have been high in recent days after a controversial vote on flying the Union flag over Belfast City Hall.
Loyalists have been holding protests across the country to show their opposition to the decision to restrict the number of days the flag is flown.
Councillors from the non-sectarian Alliance Party have been intimidated and in one case the party's offices were destroyed by fire.