The suspect, who has now been detained, is an assistant superintendent of police.
The Lagos Police Command has named its officer who shot Bolanle Raheem, a Lagos-based lawyer.
Benjamin Hundeyin, the command's spokesperson, named the killer cop as Drambi Vandi.
Mr Vandi, who has now been detained, is an assistant superintendent of police, the spokesperson said on Monday via his Twitter handle.
PREMIUM TIMES reported how Mrs Raheem, who was pregnant, was fatally shot on Christmas day by the police officer attached to the Ajiwe police division in the Ajah area of the state.
Mr Hundeyin said the suspect has been transferred to the State Criminal Investigation Department.
He also promised that the investigation into the death of the lawyer will be "swift."
Background
The incident took place at Ajah Under Bridge area of Lagos on Sunday.
Mrs Raheem's killing was, however, not the first by the police in the area.
Earlier in the month, one Gafaru Buraimoh was also shot dead by a yet-to-be-identified officer from the same division.
The latest incident has sparked widespread criticism across Nigeria.
Prominent Nigerians who have sent their condolences to the bereaved family include Lagos State Governor Babajide Sanwo-Olu, the Inspector-General of Police, Usman Baba; and a former vice president Atiku Abubakar.
Many Nigerians have also taken to social media to express outrage over the killing and call for justice for the deceased.
In a statement signed by the Force spokesperson, Muyiwa Adejobi on Monday, the Inspector-General of Police, Usman Alkali, condoled with the deceased family.
He said the action of the police officer does not represent the core values of the Nigerian Police Force.
According to the statement, the police chief has ordered a "speedy investigation and prosecution of the officers responsible for the ugly and unprofessional act, which doesn't portray the Nigeria Police Standard Operating Procedure and core values."