Justin Welby was diagnosed with mild pneumonia on Thursday and was continuing to work but after developing symptoms over the weekend he tested positive for coronavirus on Monday.
In a statement on his website, the Archbishop said he would be resting at home and avoiding contact with others over the coming days.
Buckingham Palace has been told of his regret that he will not be able to take part in the service, Lambeth Palace said.
Mr Welby was also due to light a beacon at Lambeth Palace on Thursday evening as part of The Queen’s Platinum Jubilee Beacons events, instead it will be lit on his behalf.
The Archbishop of York, the Most Revd Stephen Cottrell, will preach the St Paul's sermon on Friday instead.
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Mr Welby said: “I am deeply saddened to be missing the historic celebration of Her Majesty the Queen’s Platinum Jubilee.
“However, I will be praying for the Queen and giving thanks for her extraordinary 70 years of service to us all.
“I will also be praying for our nation at this time of celebration and thanksgiving. May the Queen’s example bring us together in unity and care for one another.”
He added that he hopes the service on Friday will inspire those watching “with the Queen’s profound commitment to fostering unity and peace among all people – and to promoting care for the natural world that God has given us”.
“Led by the love of Jesus Christ, the Queen has lived her life for the benefit of others: l pray we find inspiration from Her Majesty over the Jubilee weekend and long into the future,” he said.
“Meanwhile, as we continue to live with coronavirus, I pray too for all those who are still suffering and everyone who continues to mourn loved ones they have lost during the pandemic. May you each know the love and comfort of God.”
It is unclear if the Queen will attend the thanksgiving service at St Paul’s, but if she does there will be no ceremonial journey to the cathedral and she will use a different entrance from the steep main steps.
Wider members of the royal family are expected to be present including possibly the Duke and Duchess of Sussex and the Duke of York, and the service will be followed by a Guildhall reception for them.