Mr Kaba, 24, an unarmed black man, was shot dead by police in Streatham Hill on the night of Monday September 5 after a police chase through the streets of south London.
He also welcomed the decision of the police watchdog, the Independent Office for Police Conduct, to launch a homicide investigation last Friday.
Asked on Good Morning Britain on Friday how concerned he was about the way the incident had been handled and the way Mr Kaba’s family had been treated, Mr Khan said: “There are concerns in relation to his death by shooting by an officer.
“The independent police watchdog, the IOPC, are investigating this – not the police. That is really important in relation to how the police are policed.
“The new commissioner has taken a decision to suspend the police officer. I support that. Why? Because the public needs to have confidence in our police.
“Armed police officers do a really important job. You will see them over the course of the next few days [during the Queen’s funeral preparations]. They action firearms warrants, they respond to spontaneous incidents, they work incredibly hard.
“But when there is a homicide investigation by an independent police watchdog, I think it is right that this officer is taken off operational duties and is suspended, because that enhances public confidence, which is crucial when you police by consent.”
Mr Khan, who oversees the Met in his role as London’s police and crime commissioner, said trust and confidence in the force had fallen to “record lows” during its leadership under Dame Cressida Dick.
He said it would be “improper” to comment on the Met’s decision, prior to Sir Mark’s arrival, only to have moved the officer to desk duties for a week following Mr Kaba’s death.
He added: “There is a live investigation and the officer has not been found guilty of anything. It’s really important that the due process takes place.”
Demonstrations are planned across the country this weekend, organised by Black Lives Matter as part of the Justice for Chris Kaba campaign.
The rapper was shot after armed officers tried to stop his Audi when it activated an ANPR alert.
A single shot was fired by an officer.
Campaigners are planning to stage their London protest outside New Scotland Yard on Saturday.
Metropolitan Police Federation chairman Ken Marsh said: “It would be very challenging for us if it (the protest) were to take place.
“But we would be able to deal with it if it did. We are in a period of mourning for the Queen. The whole country is taking part in it.
“It would be more helpful if a protest wasn’t this weekend, but people have the right to demonstrate.
“We will police anything like that without fear or favour.”
Crowds marching to Scotland Yard last Saturday paid tribute to the father-to-be.
Signs reading ‘Black Lives Matter’, ‘Justice for Chris Kaba’ and ‘Abolish the Met’ were held up as speakers using a megaphone led chants of ‘no justice, no peace’ and ‘police are the murderers.’
Demonstrators assembled on Parliament Square and made their way through Whitehall.
Rapper Stormzy attended the march and backed the family’s campaign.
He told the crowd: “I encourage everyone to strive for stamina. Nobody should be able to go on like this,’ he said. ‘They were responsible for the death of someone.
“That is [possibly] murder. It could have been either a brother or a nephew.”
Wretch 32, another British rapper, was also present for the rally. He said: “Why is our law superior to the law? Without justice, there is no peace.”
The IPOC on Thursday agreed to demands from Mr Kaba’s family to view the police bodycam and helicopter footage of the shooting and the lead up to the firing of the fatal shot.