The Olympic fencer was picking up an identification badge at the interactive, film and music event on Saturday when a volunteer told her she must take off her hijab before her photograph could be taken.
"Even after I explained it was for religious reasons, he insisted I had to remove my hijab," she said on Twitter.
SXSW organizers said on Sunday in an email to Reuters that they have since removed the volunteer for the duration of the event.
"We are embarrassed by this and have apologized to Ibtihaj in person, and sincerely regret this incident," SXSW said in the statement.
Muhammad, 30, will make history in Rio de Janeiro as the first Olympian to represent the United States wearing a hijab.
Muhammad has become an outspoken critic of presidential candidate Donald Trump, who called for a ban on Muslims from entering the United States.
"I feel like I owe it to people who look like me to speak out," Muhammad told reporters on Wednesday. "When I hear someone say something like, Were going to send Muslims back to their countries, I say, Well, Im American. Where am I going to go?"
After the incident was resolved at the event, Muhammad said that she was issued the wrong identification.
"I was given the wrong ID! From now on my name is Tamir & I work for Time Warner Inc" she tweeted.