The garment is part of an exhibition at the National September 11 Memorial & Museum portraying the decade-long hunt to find the al Qaeda mastermind behind the 9/11 attacks.
The black and brown uniform shirt worn by the anonymous Team Six member during the daring raid on bin Laden's compound in Abbottabad has a US flag patch on the sleeve.
But the decision to display the SEAL shirt has been criticised.
Newsweek said the exhibition was out of place, "short-circuiting the grief that rightly haunts these galleries," a tribute to the nearly 3,000 people killed in the September 11, 2001 terror attacks on New York and Washington.
"The good guys won, it says triumphantly... But that's cheap closure, and it seems crass to parade the evidence of our victory in what should be a space for somber, silent thought and prayer," it wrote in an article.
The museum defended the move.
"This exhibit not only captures a seminal moment in American history, it also allows millions of visitors the chance to recognize the extraordinary bravery of the men and women who sacrifice so much for this country," 9/11 Memorial President Joe Daniels said.
The exhibition also includes a "challenge coin" donated by "Maya," the alias for the CIA operative who pursued the al Qaeda leader, and a brick recovered from the bin Laden compound.
The brick, donated by a Fox News journalist, has been on show since the museum opened its doors to members of the public in May.
The challenge coin was created to commemorate the operation and is marked with May 1, 2011, the date in the United States when bin Laden was killed - in the early hours of May 2 in Pakistan.
The other side shows a red "X" in reference to the red X that president George W Bush put through the names of key al Qaeda operatives after they were found, arrested or killed, the museum said.
The museum, built into the bedrock of the World Trade Center Twin Towers, documents the attacks, their impact and legacy with 10,000 artifacts.
Daniels said he had had "the distinct honour" to meet the man who wore the shirt into the airborne raid on bin Laden's home.
"I thank him and 'Maya' - both for their bravery, courage and determination, which provided a measure of justice for every single American, and for entrusting us with these artifacts of such national and international importance," he said.
More than 900,000 people have visited the museum since it opened and more than 15 million have visited the outside 9/11 Memorial, which opened three years ago.
COMMENTS (5)
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Does the museum have any OBL postmortem results and DNA evidence?
WOW - Is it that world's No1 Military is scared to release Navy Seals name and photos who were part of Abbottabad operation. World will only love them more and respect them more if they come on TV.
I thought the Osama raid was a myth created by the media, CIA, RAW & Mossad!
May or may not be, who can tell, it is not like muellers or neymars shirt from World cup, and us dod lies like no one else.
Hey didn't all these seals die in a helicopter crash in Afghanistan?