The Brumbies are the only side to have qualified from the Australian conference for the Super Rugby quarter-finals and the duo were injured in Friday's 16-15 loss to the Queensland Reds.
Toua has been ruled out for between four to six weeks after being diagnosed with a grade one high ankle sprain while Godwin is expected to miss up to three months after being taken off in the second half with a knee injury.
"We are disappointed for the guys who have done so much for us this year," head coach Stephen Larkham said in a Brumbies statement.
"The boys may not be able to take to the park in finals but they will certainly take part in the preparation with the rest of the team."
Flanker Chris Alcock sustained a deep gash to his thigh but is expected to be in contention for the knockout game at home against the Highlanders on July 21, the Brumbies added.
Wallabies lock Rory Arnold suffered a shoulder injury but has recovered well and will be in contention for the last-eight clash.
(Reporting by Sudipto Ganguly in Mumbai; editing by Amlan Chakraborty)
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