"I was just asked to remove my hijab at SXSW Registration for my ID badge. I can't make this stuff up," Ibtihaj Muhammad tweeted from the Austin, Texas, event.
She continued, "Even after I explained it was for religious reasons, he insisted I had to remove my hijab for the photo to receive my badge."
But, Muhammad said, she didn't even receive the correct badge – and was instead given the badge of someone with a similar-sounding name.
"From now on my name is Tamir & I work for Time Warner Inc," Muhammad tweeted with a photo of her badge.
SXSW said in a statement to PEOPLE that it was "embarrassed" and that the incident was the work of "one volunteer who made an insensitive request and that person has been removed for the duration of the event.
"We are embarrassed by this and have apologized to Ibtihaj in person, and sincerely regret this incident."
I was just asked to remove my hijab at SXSW Registration for my ID badge.. I can't make this stuff up #SXSW2016— Ibtihaj Muhammad (@IbtihajMuhammad) March 12, 2016
Even after I explained it was for religious reasons, he insisted I had to remove my hijab for the photo to receive my badge #SXSW2016— Ibtihaj Muhammad (@IbtihajMuhammad) March 12, 2016
Muhammad – who could not immediately be reached for comment by PEOPLE – is a star of the American fencing scene, with sponsors including Visa and American Airlines, according to USA Today.
She is thought to be the first American Olympian to compete while wearing a hijab.
Indeed, it was the fact that fencers compete while completely covered that first drew Muhammad to the sport, she told the New York Times.
Growing up, she played softball, tennis, track and others, and her mother "regularly adjusted uniforms," according to the Times, as the family's faith required Muhammad's arms and legs be covered.
"My parents were on a mission to find a sport without alteration," Muhammad told the paper.
She added that wearing her hijab with her fencing uniform "is not something I've ever really thought about."
"I get asked about it a lot," she told the Times. "People ask Muslim women about it – not just athletes – all the time. Like, aren't you hot? On a hot day, you'd still wear a shirt and pants. I would not leave the house without it."