The arena, which will be home to the Leicester Riders, is a joint venture between the team, Leicester College and the city council.
Construction started on the £4.5m venue earlier this month at a derelict site in Charter Street.
Sport England said it hoped the arena would provide an opportunity for more people to play sport.
The 2,000-seat arena will also be home to the Leicester Cobras wheelchair basketball team and will include a fitness suite.
Sport England said it was supporting the project because it will "help meet the sporting needs of the city" by creating facilities for large indoor events and encouraging people to take up sport.
Leicester Community Sports Arena Limited (LCSAL), which will lease the building, said it was "delighted".
Kevin Routledge, director, said: "Increasing regular participation in sport is a key target for the arena and the Riders, and we believe this investment will be pivotal for the city and the county in that regard, and in particular, for young people."
He said it was confident the arena would be used by local people for all sporting activities when it opened later this year.
The Leicester Riders Basketball Club was founded in 1967 and is the oldest professional club in British basketball.
A new basketball arena being built in Leicester has been given £1.25m funding from Sport England.