The 34-year-old, from Liverpool, was arrested on suspicion of assisting an offender after he was stopped by officers on the M42 near Leamington Spa in Warwickshire, Merseyside Police said.
He was the fourth man to be arrested in the space of 24 hours by officers investigating the death of nine-year-old Olivia, who was shot in her home in Dovecot, Liverpool on August 22.
A police spokesman said the vehicle the man was driving was seized following his arrest on Sunday evening.
A 34-year-old man from Liverpool was arrested in the Runcorn area in the early hours of Sunday on suspicion of murder and attempted murder.
Olivia Pratt-Korbel was fatally shot at her home
Family Handout
Two other men, a 41-year-old from Knowsley and a 29-year-old from Liverpool, are being questioned on suspicion of assisting an offender.
Warrants were executed at two properties in Liverpool on Sunday, police said.
Olivia died after she was shot in her home when a gunman chased convicted burglar Joseph Nee into the property at about 10pm.
A post-mortem examination found her medical cause of death was a gunshot wound to the chest.
Her mum Cheryl was also injured.
Flowers lined the streets near the scene of Olivia's killing
Peter Byrne
Detective Chief Superintendent and head of investigations Mark Kameen said: “I continue to urge anyone who has information that can help our investigation into Olivia’s tragic murder to please come forward so we can bring those responsible to justice.
“A number of people have been arrested in respect of this investigation.
“However, we still need the public’s help in ensuring that we can a build a strong evidential picture so justice is served for Olivia and her family.
“With this, I appeal for those who may have information, no matter how small, that could continue to help our inquiries to contact us directly or anonymously and we will do the rest.”
A 36-year-old man from Huyton and a 33-year-old from Dovecot who were arrested on suspicion of murder and two counts of attempted murder in relation to Olivia’s death have been released on bail.