Six other people had been arrested but were released without charge.
Ten men remain in custody for questioning, while a total of e ight people have now been released without charge, Greater Manchester Police said.More news: Korea's ICBM and nuclear weapons nears completion
Residents have been evacuated from the Rusholme area of the city and a 100-metre cordon put in place while officers assess the white Nissan Micra.
"This is potentially a significant development in the investigation", Detective Chief Superintendent Russ Jackson said in a statement, which added that enquiries concerning the vehicle were ongoing.
Police say they are very interested in the movements of the auto and who was in it over the past few months.More news: Japan, France welcome US leadership in the Asia-Pacific
Buckley was off duty and waiting for his 15-year-old daughter Stephanie when the bomb exploded.
As part of the investigation, authorities are also asking the public to help track down a blue suitcase Abedi was seen with in the days leading up to the attack.
Earlier Ariana Grande arrived in the United Kingdom, ahead of Sunday's benefit concert for the victims of the Manchester terror attack.More news: DUP leader Arlene Foster to hold talks at No10 with Theresa May
The Duke of Cambridge also visited Manchester on Friday and met police officers and volunteers before paying a visit to Manchester Royal Infirmary to meet some of those injured in the attack.