Dhawan fell on his left shoulder in the fifth over of the match as he dived to stop an Aaron Finch drive at cover point. Nitin Patel, the team physio who attended to him, took him off the field.
Dhawan was immediately sent for an X-ray. When he returned to India's dressing room, he was seen with his left arm in a sling. Virat Kohli said at the post-match press conference that Dhawan was in "no position to strike the ball."
A BCCI spokesperson said reports of Dhawan's scans had been received by the physio and "he will be assessed overnight, before a final update of his injury will be issued".
KL Rahul, who made a match-winning 52-ball 80 from No. 5 in the second ODI in Rajkot, opened instead of Dhawan. His partner Rohit Sharma, incidentally, had also bruised his shoulder while fielding during the Rajkot ODI and was a doubt for the Bengaluru game.
In the same game, Dhawan had bruised his ribcage after trying to negate a Pat Cummins delivery, but continued to bat on and make 96 in India's series-levelling victory. He spent the entire duration of the Australia innings off the field to take care of the injury.
Dhawan has hit a purple patch in recent times, scoring 52, 74 and 96 in his three most recent international innings. In November, he picked up a freak injury - "a deep cut on his left knee" - during a Syed Mushtaq Ali Trophy T20 game for Delhi against Maharashtra. Originally picked for the series against West Indies, he was later withdrawn as the medical staff felt he needed more time for his stitches to come off and the wound to heal.
As things stand, Dhawan is part of India's T20I squad for the tour of New Zealand starting January 24. India are set to fly out of Bengaluru early on Monday to Auckland via Singapore.