The explosion, which also wounded dozens of worshippers, tore through the al-Bolayli mosque in the morning hours, according to Yemeni security officials.
The mosque is located in an area where many residents support the Shiite rebels, also known as Houthis, who have controlled Sanaa since last September.
The IS affiliate's claim of responsibility came in a statement circulated on Twitter by the Sunni militant group's supporters.
The security officials said the suicide bomber placed an explosive device in his shoe, causing an initial explosion. As worshippers rushed to the door, he detonated himself in the middle of the crowd, they said.
Also Read
The officials, who remain neutral in the conflict that has splintered the country, spoke to the AP on condition of anonymity because they were not authorized to talk to the media.
There were puddles of blood and debris outside the mosque, whose ornate facade was damaged by the blast. Police and some Houthi fighters came to inspect the aftermath. Eid al-Adha is a major Muslim holiday, also known as the Feast of Sacrifice.
The Islamic State affiliate in Yemen has claimed responsibility for a series of suicide bombings in Sanaa targeting Shiites in the past months. American officials initially expressed skepticism that the affiliate existed, as Yemen is also home to the world's most dangerous al-Qaeda offshoot.