The 41-year-old man was detained in west Belfast on Tuesday evening.
Two men aged 25 and 34, who were arrested in the Belfast area on Monday evening, are also being questioned by police.
The PSNI officer, his wife and two young children were about to leave their Upper Newtownards Road home for lunch on Sunday when the bomb was discovered.
Detectives from the PSNI's Serious Crime Branch are investigating the attempted murder.
Senior Investigating Officer Detective Inspector Dickson said: "At this stage we believe that the device was left underneath the officer's car sometime between 5.30pm on Friday 28 December and 2pm on Sunday 30 December.
"My investigation team want to speak to anyone who was in the area of the Upper Newtownards Road between the junction of the Knock Road and Knockdene Park."
Police particularly want to speak to anyone who may have seen something untoward in that area, like a parked vehicle or someone acting suspiciously.
Detectives can be contacted in Ladas Drive on 0845 600 8000. Information can be given anonymously to the independent charity Crimestoppers on 0800 555 111.