The festival was founded in 2005 and is usually held on or near 6 August, Jamaican Independence Day.
In recent years the event, which is free, has attracted up to 15,000 people and closed roads in the area.
The organisers said they were “incredibly disappointed” by the decision.
Lambeth Council refused their application to hold the event this year, saying in a statement the 2015 event drew “a large number” of complaints from local residents.
The council stressed that the cost of policing and cleaning up afterwards “ran into hundreds of thousands of pounds”.
A council spokeswoman said: “Sadly, last year’s event became a victim of its own success and we need to pause it for this year, let the community take it back to its roots as a safe, fun event for everyone with professional organisation.”
The founder of the festival, Ros Griffiths, joined the council in appealing for more people to get involved in order to ensure the event could go ahead in 2017.
She said: “The community needs to reclaim this as a celebration of Brixton, not a free-for-all that creates chaos, mess and unease.”
But organisers who were in the process of planning this year’s Brixton Splash spoke out against the decision, saying they feared it did not fit with the council’s “gentrified image” of Brixton.
Brixton Splash director Shezal Laing claimed: “We’ve been trying to ensure we plan a safe event, we’ve been seeking meetings with the council and other stakeholders, including the police, and at every level we’ve been blocked.” Article courtesy http://www.bbc.co.uk/