The Labour leader, a lifelong republican, had the chance to attend a meeting of the ceremonial body which formally advises the monarch – but declined, citing “prior engagements”.
A spokesman refused to give details of the events, saying only that they were “private”, but sources close to Mr Corbyn insisted it was not intended as a snub.
It was confirmed meanwhile that he will attend a State Banquet at Buckingham Palace later this month in honour of Chinese President Xi Jinping along with other senior politicians.
Guests at the white tie dinners are traditionally received by the Queen and the Duke of Edinburgh, shaking their hands and exchanging a few words of greeting.
Earlier it was reported that Mr Corbyn could avoid the need to swear an oath of allegiance in the presence of the Queen through a mechanism known as an Order in Council.
The Daily Telegraph said the Privy Council – including the monarch – could agree to appoint him as a new member without him being present.
In order for that to happen, the paper said he would still have to confirm that he had taken the oath but would not have to kneel before the sovereign.
Nevertheless, such a move would be highly controversial at a time when the Labour leader has seen his loyalty to Britain fiercely challenged by opponents.
He was widely criticised after he did not sing the national anthem at the Battle of Britain 75th anniversary commemorations.
In his speech to the Conservative Party conference on Wednesday, Prime Minister David Cameron accused him of a “Britain-hating ideology”.
Tory MP Sir Alan Duncan, himself a privy councillor, said: “The Queen has always put herself above politics but Jeremy Corbyn seems to want to put his politics above the Queen.
“This is not so much about snubs, insults or ceremonies – it is more about whether Jeremy Corbyn wants to be a serious political figure or just a perpetual rebel.”
Mr Corbyn was invited by Mr Cameron to join the Privy Council on becoming Labour leader last month.
Although its functions are largely ceremonial, membership does enable him to receive confidential intelligence briefings.
While Mr Corbyn is clearly uncomfortable with the more formal aspects of his role as Leader of the Opposition, his decision to attend the banquet for the Chinese president underlines how difficult they are to avoid.
The dinner will take place amid the splendour of the Palace Ballroom, and the guests will eat off antique china and drink from crystal glasses originally made for the Queen’s Coronation in 1953.
The “recommended” dress code for men is white tie and tails, although it is not compulsory. A source close to the Labour leader said he had “no idea” what he would be wearing.
A spokesman for Mr Corbyn later played down his decision not to attend the Privy Council.
“Although Jeremy was unavailable for today’s meeting, he has confirmed he will be joining the Privy Council,” the spokesman said .
“As the Prime Minister and others did, it is far from unusual to miss the first meeting due to other commitments.”
According to Cabinet Office records, Mr Cameron was made a privy counsellor shortly after becoming Conservative leader in December 2005, but was not sworn in for another three months.
Constitutional expert David Rogers – who has written a forthcoming book: By Royal Appointment: Tales from the Privy Council – said while a member could be sworn in by an Order in Council, they had only been used when the individual concerned was physically unable to attend.
“I have never come across a case where an Order in Council has been made so somebody can become a privy counsellor because they didn’t want to go to the meeting,” he told BBC Radio 4’s The World at One.
The Queen held the Privy Council meeting at Buckingham Palace at 5.30pm.
Among those present was the Leader of the House of Commons Christopher Grayling, Paymaster General Matthew Hancock, Business Secretary Sajid Javid and Amber Rudd the Energy and Climate change Secretary.
The MPs James Brokenshire and Gisela Stuart were sworn in as members of the Privy Council.