Apache said production at its Stag oil field and the BHP Billiton-operated Pyrenees field had been shut-in.
It added that the repeated cyclone-related interruptions meant repairs to the Van Gogh production facility would now be completed by the end of the first week of February with production resuming soon after.
Meanwhile, Dow Jones Newswires quoted Chevron as saying it had evacuated some non-essential personnel from its Barrow and Thevenard Island oil and gas operations and was monitoring the path of the tropical low closely.
The supermajor added that production was being shut-in and wells secured.
A Woodside spokesperson was quoted by The Australian as saying that the Perth-based company had shut-in production from the Cossack Pioneer and Enfield fields, while Santos has moved its Mutineer-Exeter floating storage and offloading vessel to avoid the cyclone.
The Bureau of Meteorology said winds at Bianca were intensifying and that the cyclone was following a westerly course overnight, bringing the system away from the Pilbara coast.
The Fire & Emergency Services Authority of Western Australia warned that while the cyclone was moving west at 17 kilometres per hour, damaging winds with gusts to 120kph were possible between Roebourne and Onslow.