"International and domestic terminals are experiencing some flight delays. Please contact your airline for more information," the airport tweeted this morning.
One passenger tweeted a photo of massive at Sydney airport, adding: "It's mental."
Melbourne Airport is also reducing the number of flights arriving and departing.
Qantas and Virgin Australia are warning their passengers of delays in both cities.
"Sydney and Melbourne Airports have reduced the number of flights allowed to arrive and depart each hour, which is impacting all airlines," Virgin Australia said in a statement.
"This may also affect flights arriving and departing into other destinations across the network.
"Virgin Australia is working hard to minimise delays for passengers, and get everyone on their way as quickly and safely as possible."
Qantas said it was monitoring the situation and advised passengers to make sure their contact details were included in their flight booking in case they needed to be contacted about flight changes.
Frustrated flyers have taken to social media as they await news of their flight status, with many of them feeling their second day of travel disruption after yesterday's airport delays.
Passengers flying today are advised to check in with their airline before heading to the airport.
The Bureau of Meteorology has issued a gale warning for the Sydney coast and a strong wind warning for Sydney closed waters.
It's the second day Sydney airport has been impacted by strong winds that swept a massive dust storm across the city yesterday.
A thick line of dust "the size of Tasmania" stretched almost the entire length of NSW yesterday as strong winds from a low pressure system whipped up masses of dirt across the drought-stricken state.
A line of dust more than 500km long could be seen from the Victorian border, through Canberra and up to Queensland.
The strong winds delayed flights at Sydney Airport for most of yesterday.
