The ex-Labour leader, who was in power from 1997 to 2007, was given the title as the New Year's Honours were awarded.
But the petition complains that his role in the Iraq war makes him "personally responsible" for many deaths and accuses him of "war crimes".
Labour leader Sir Keir Starmer said Sir Tony had "earned" a knighthood.
On 1 January, Sir Tony became a member of the Order of the Garter, England's oldest and most senior order of chivalry.
The appointment was the personal choice of the Queen, who has up to 24 "knight and lady companions", with current Prime Minister Boris Johnson not involved in the decision.
But a petition posted on the change.org website by actor and presenter Angus Scott says Sir Tony "caused irreparable damage to both the constitution of the United Kingdom and to the very fabric of the nation's society" while in office.
"He was personally responsible for causing the death of countless innocent, civilian lives and servicemen in various conflicts. For this alone he should be held accountable for war crimes," it adds.
"Tony Blair is the least deserving person of any public honour, particularly anything awarded by Her Majesty the Queen."
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