The Finn, who had qualified sixth at Albert Park, felt pain during Saturday's qualifying session and was taken to hospital for scans.
Williams said the scans showed Bottas had suffered a small tear to the annular part of a disc in his lower back.
"Valtteri has since been evaluated by the FIA's medical team and following a series of tests, the FIA Medical Delegate has deemed Valtteri unfit to take part in this afternoon's race," they added.
"The team respect the FIA's decision and will now work with Valtteri ahead of the Malaysian Grand Prix (on March 29) to ensure he receives the treatment required to get him back to full fitness."
Bottas enjoyed a breakthrough season in 2014, securing six podium finishes for Williams to claim fourth place in the championship.
The 25-year-old said he was confident he would able to resume driving for the next race.
"I have done a lot of work since the issue with my back came in qualifying to get myself ready, starting treatment immediately, so the news that I couldn’t race today was obviously disappointing but I respect the decision," Bottas said.
"I now have two weeks until the next race to receive further treatment to ensure I will be back to full fitness and even stronger in Malaysia.
"I’m very eager to get back in the car and race because the FW37 is looking competitive and I’m confident we can fight for podiums."
Williams do not have a reserve driver at present, with Britain's Susie Wolff -- wife of Mercedes motorsport head Toto -- serving as a tester and Alex Lynn as a development driver.
Brazilian Felipe Massa finished fourth for Williams in Sunday's race after starting third on the grid.
(Reporting by Julian Linden; Editing by John O'Brien/Peter Rutherford/Alan Baldwin)
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