Police believe it was planted by "violent dissident republicans".
The device - which police described as more intricate than a pipe bomb - was reportedly discovered under a car at Ardanlee, in the Culmore area of the city, on Wednesday morning.
Children were in the area at the time, police said.
Police have not confirmed whether anyone was injured in the blast.
Debbie Watters, vice-chairwoman of Northern Ireland's Policing Board, said the officer had had a "very lucky escape".
The area remains cordoned off and a number of homes have been evacuated in an ongoing security alert.
The device was intended to kill and inflict harm in the community, said the PSNI's Supt Gordon McCalmont.
"This was an attempt to kill one of my colleagues," he said.
"My thoughts are with my colleague and his family. You can imagine the impact this trauma will have on them."
Ms Watters said she was grateful that the "evil intent" of those responsible had not succeeded
"Such activity reinforces the continuing threat that exists for our police officers both on and off duty," she said.
"As a community, it is our responsibility to ensure those behind such activity are brought to justice."
Police have extended the security cordon to all of Spruce Meadows and part of Ardanlee while the investigation continues.
Residents who were asked to leave the estate are using the nearby St John's Parish centre until they are allowed to return home.
Mary Davey, who lives at Ardanlee with her three young children, said she was shocked by the incident.
"We looked out the window and saw the police cars arriving with the lights flashing and then the tape going over across the front of the estate," Mrs Davey told BBC Radio Foyle.
"We're very angry, they're putting everyone's life at risk, not just the people they are targeting."
Her husband, Barry, said they had lived in Derry peacefully for 20 years.
"We have three young children here and I'm from Belfast, so where we can actually go is very limited," he said.
"We're anguished because this is not daily life for us. We came here thinking we would have a quiet life, people don't want this."
Meanwhile, in a separate incident, homes were evacuated in County Tyrone after the discovery of a pipe bomb at Sion Mills.
Police have not linked the two incidents.
The Sion Mills security alert ended shortly before 17:00 GMT.
A bomb has exploded outside the home of a serving police officer in Londonderry as Army technical officers were trying to defuse it.