Manyama sustained the injury in a car crash when travelling from training on Tuesday afternoon.
“Lebo went through MRI scans yesterday and that revealed a fractured elbow. He will accordingly be treated and be put under a recovery plan,” Chiefs' physiotherapist David Milner told the club's website.
Meanwhile, striker Leonardo Castro and new signing Andriamirado 'Dax' Andrianarimanana are still out with their respective knocks, while Zimbabwean playmaker Khama Billiat hurt his back on international duty.
“Both Castro and Dax are progressively improving,” said Milner.
“Castro is recovering from an ankle injury, while Dax had a calf strain.”
He added: “Khama has to be assessed for a back injury.”
There is some positive news as winger Joseph Molangoane is now off crutches and in full rehabilitation.
He broke his leg during his team's 3-0 win over Free State Stars in the MTN8 quarter-finals on August 11 after coming off second best in a challenge with Makhehleni Makhaula.
Amakhosi next host Black Leopards in the Telkom Knockout last-16 at FNB Stadium on Sunday (15h30).
The Glamour Boys will resume their league campaign with the Soweto Derby against Orlando Pirates at the same venue on October 27.