Photos show Macklemore wearing a black wig and beard with a fake hooked nose at the May 16 show at the EMP Museum.
Macklemore said the costume pieces worn were randomly chosen to disguise himself and allow him to move freely during the show. He denied that the costume was meant to be a caricature of a Jewish man.
"The character I dressed up as on Friday had no intended cultural identity or background. I wasn't attempting to mimic any culture, nor resemble one," Macklemore wrote.
"I respect all cultures and all people," he wrote. "I would never intentionally put down anybody for the fabric that makes them who they are. I love human beings, love originality, and ... happen to love a weird outfit from time to time," he added.
On Sunday, actor Seth Rogen tweeted about the incident.
In a Tweet to Seth Rogen, Macklemore wrote: "A fake witches nose, wig, and beard = random costume. Not my idea of a stereotype of anybody."
Rogen replied: "Really?? Because if I told someone to put together an anti-Semitic Jew costume, they'd have that exact shopping list."
Macklemore wrote in his post that he understood his critics' point of view.
"I truly apologize to anybody that I may have offended," Macklemore wrote.
Macklemore & Ryan Lewis gained widespread fame with a message supporting diversity, and their hit song "Same Love" calls for tolerance and support for members of the gay community.
The two performed the song at January's Grammy Awards while several same-sex couples were married, and they have been lauded for their progressive messages.
The Associated Press contributed to this report.