The Unites States also says South Africa has used unwarranted sanitary restrictions to keep out US pork and beef.
South Africa says it is taking the warning seriously and is working to find a solution.
Trade Minister Rob Davies told reporters in Cape Town that they are "pretty close to resolving the sanitary matters that were outstanding".
The BBC's Lerato Mbele in Johannesburg says high-value goods such as cars remain unaffected by the latest dispute.
South Africa could still avoid the suspension, which could cost it up to $7m (£5m) in lost trade, if it meets benchmarks to eliminate barriers to US poultry, pork, and beef, said US Trade Representative Michael Froman.
"We do not take this decision lightly, and, in fact, have been working hard over many months - indeed years - to help South Africa avoid such action. Unfortunately, the issues persist," Mr Froman said in a statement.
Eliminating barriers to US trade and investment is one of the criteria for membership of the African Growth and Opportunity Act (Agoa), which was renewed earlier this year and provides duty-free access to goods from sub-Saharan African countries, ranging from crude oil to clothing.
Analysis: Matthew Davies, BBC Africa Business Report
These are warning shots in a dispute which both sides would like to see go away.
However, trade disputes are never straight-forward, but tend to be convoluted games of chess and this one is no exception. There's much posturing at the moment.
South Africa's trade minister Rob Davies says: "When someone says jump, you don't say 'How high?', you negotiate." These sorts of warning shots are negotiating tactics; an attempt to speed the process along.
But if the Americans are trying to force the South Africans to accept their poultry exports, they may be going about it the wrong way.
The South African government is adamant that the delay lies not with them, but with the independent vets looking into whether or not the imported US birds are safe.
Nonetheless, missing the 15 October deadline to agree new animal health rules infuriated the Americans. But is this a slippery slope to South Africa being kicked out of Agoa? That would seem very unlikely.
What is far more likely is that a deal will be done within two months. But even in its absence, it's still a long road to Agoa exit.
The South Africans know this and are in no mood to jeopardise the billions tied up in their car industry which gains significant advantage from exporting tariff-free into the US. The investment figures in South Africa's automotive sector are not chicken feed and are unlikely to be risked in a trade spat.