Police were called to a shooting on Lord Warwick Street on Thursday (April 2) at 3.40pm.
Eghosa Ogbebor was found with serious injuries and died at the scene.
Yesterday (April 4), a 46-year-old man was arrested on suspicion of assisting an offender and remains in custody.
A 16-year-old boy and 19-year-old man were arrested in Woolwich on suspicion of murder.
Detective Chief Inspector Lucie Card, whose team is leading the investigation, said: “Our team of dedicated detectives are continuing enquiries to investigate Eghosa’s tragic death.
“Residents in Woolwich may have noticed a large amount of police activity last night, as officers arrested three further people in connection with the investigation.”
Residents reported being ordered to stay indoors and shared pictures on social media of armed police in the streets near Woolwich Dockyard.
Six people have been arrested in total in connection with the incident.
Two boys, aged 14 and 16 and an 18-year-old man, were arrested on April 3 and were released on bail.
Detective Chief Inspector Lucie Card, whose team is leading the investigation, said: “Our team of dedicated detectives are continuing enquiries to investigate Eghosa’s tragic death.
“Residents in Woolwich may have noticed a large amount of police activity last night, as officers arrested three further people in connection with the investigation.
“We appreciate the concern that Eghosa’s death has caused, particularly among the local community who will continue to see an increased police presence around the area.
“There may be people who have heard information or witnessed suspicious activity in the area but not yet contacted police.
“We urge these people to contact us and assist with the investigation.
“We will continue to support and update Eghosa’s family as the investigation continues and our thoughts remain with them at this incredibly difficult time.”
Anyone with information or footage is asked to call police on 101, quoting CAD 4848/2APR, or independent charity Crimestoppers, anonymously, on 0800 555 111.