The opener was hit by a Josh Hazelwood delivery in a chilling blow yesterday that saw him drop to his knees and let go of his bat, with captain Steve Smith rushing from slips to check on his deputy.
Appearing shaken, Warner removed his helmet and immediately walked off the field leaving his bat behind.
Cricket Australia's news site cricket.Com.Au said the fiery left-hander had passed a concussion test and would be available for the tour of Bangladesh, but would sit out the rest of the intra-squad match in Darwin, Australia's Northern Territory.
A focus on player safety has been heightened since the tragic death of Australian batsman Phillip Hughes.
Hughes, who played 26 Tests, died from bleeding on the brain in November 2014 after being hit on the base of the skull by a rising ball at the Sydney Cricket Ground during a domestic match.
The Australian squad flies to Dhaka on Friday for the two-Test tour which begins on August 27.