Bouchra Bagour, 35, was on trial in Avignon on charges of defending terrorism after sending her boy, named Jihad, to his school in the town of Sorgues wearing the T-shirt.
Bagour and her 29-year-old brother Zeyad, who was also charged and acquitted, had faced up to five years in prison and a fine of 45,000 euros ($59,000) if convicted.
The court ruled that prosecutors had not proven that the defence of terrorism was "unequivocal", as required by the law.
"I am delighted, it was a discerning and legally justified decision that should put an end to this unfortunate affair," said Gaele Guenoun, the lawyer for Bagour, who was not present for the ruling.
Bagour had admitted to the court that sending her child to school wearing the T-shirt had been "tactless" but insisted it was not meant as a provocation.
She said she simply wanted to make note of her son's birthday on September 11 and did not intend to reference the 9/11 attacks in the United States in 2001.
Her brother, who had also faced charges for having bought Jihad the T-shirt, said after the ruling that he was "happy" and "relieved".
In an earlier hearing both of them had pleaded their innocence in court, claiming they thought the T-shirt would “make people laugh”.
“For me the text is simply my son’s name and his date of birth,” Bagour had said. “It’s a bit different but I thought it would make people laugh.
“My brother gave my son the sweatshirt, I put it on him, and I never thought anything of it.”
For his part, the uncle Zeyad, 29 had told the court: “I had no intention of being provocative or shocking people.
“For me the words ‘I am a bomb’ mean ‘I am beautiful’”.
But his excuse did not hold water with the lawyers for the Mayor of Sorgues.
“Idiocy is often the best alibi to hide our real intentions,” Claude Avril said in the earlier hearing. “The most scandalous aspect of this is the manipulation of a three year-year-old to convey the words of terrorism.”
The mother and uncle of the boy, who official records show was born on September 11, 2009 and was given Jihad as his first name, were not known Islamists, prosecutors said.
Sorgues Mayor Thierry Lagneau, who had expressed outrage at the incident, said the court ruling did not reflect the wishes of the local community.
"I have the feeling that the law does not reflect reality as it is seen by citizens," he said, adding that the ruling "gives the impression that everything is allowed."