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The match officials were ready to wait until 6 pm for light to improve, but a slight drizzle put paid to the wait and the day was called off at 5.20 pm local time.
Harris (79) scored his second Test half-century in the morning session, but was out within three overs on resumption, playing on to his stumps off Ravindra Jadeja.
Presenting the best and worst from the third day's play at Sydney Cricket Ground.
Australia threw away a good start after Kuldeep, Jadeja combined to pick five wickets to out India on top.
Having played out a fine morning session, Australia were pushed back by India, who dealt the hosts four big blows, keeping them to 198/5.
Harris dominated a stand of 72 with Khawaja and with Labuschagne put on 50.
Opener Aaron Finch, who has scored only a single half-century in three Test matches, might be axed from the playing XI and as per reports, did not bat in the nets.
According to Waugh, Marcus Harris and veteran Shaun Marsh should open the batting, followed by incumbent Usman Khawaja.
Former captains Steve Waugh and Ricky Ponting want out-of-form opener Aaron Finch to be dropped from Australia's playing eleven.