Scotland Yard said there was “nothing to suggest” the 27-year-old mother-of-two was targeted in the shooting in Peckham in the early hours of Sunday morning despite claims.
Ms Johnson remains in hospital in a “critical” condition, with “very serious” injuries as detectives investigate the attack.
Metropolitan Police Commander Alison Heydari said: “From our inquiries so far, we have established that Sasha had been at a party at a house on Consort Road in Peckham early on Sunday morning.
“Around 3am, a group of four black males dressed in dark coloured clothing entered the garden of the property and discharged a firearm. They had left the scene before officers arrived.”
Ms Johnson emerged last year as a prominent figure in the Black Lives Matter movement and has been described as “a strong, powerful voice for our people and our community” by the Taking The Initiative Party, of which she is a member.
The political party said Ms Johnson had “received numerous death threats as a result of her activism,” but police have downplayed fears she may have been targeted.
Ms Heydari said: “We are aware of Sasha’s involvement in the Black Lives Matter movement in the UK and I understand the concern this will cause to some communities – however I wish to stress that at this time there is nothing to suggest Sasha was the victim of a targeted attack.
“We are also not aware of any reports of threats made against her prior to this incident.”
Friends of Ms Johnson have suggested the shooting may have have been gang-related.
Imarn Ayton told BBC News: “There was a rival gang that may have heard about someone being in that party that they didn’t feel quite comfortable with or trusted and so they resorted to driving past and shooting into the garden, and one of those shots obviously hit Sasha Johnson.
“But I don’t believe she was the intended victim.”
As the search for the attackers continues, superintendent Kris Wright appealed to the community, calling on people to “do the right thing” and saying: “If you have any information that could assist this investigation, no matter how small you think it is, then please contact police or the independent charity Crimestoppers.
“Sasha has been left critically injured and her family is distraught; the people who have carried out such a callous attack do not deserve to be protected and must be apprehended.
More than 150 people attended a vigil for Ms Johnson in Ruskin park, south London, on Monday.
Black Lives Matters UK said it was shocked at the shooting of “a young mother and fearless political campaigner who was at the forefront of many BLM protests last summer”.
It explained that although she was not formally part of the BLM organisation, “she impressively founded a new black-led political party and was dedicated to resist anti-black racism”.