"A bomber blew himself up inside the cultural center in the Ibb city as Houthis were holding a ceremony to mark the birth of Islam's prophet," a security source told The Anadolu Agency.
They said at least 23 bodies, including women and children, had been transferred to two hospitals in the city of Ibb.
In a text message, the state Saba news agency cited the head of Ibb's police as saying three people had died and 30 had been wounded.
Residents reported there was a second explosion outside one of the two hospitals, al-Thawra. No details were immediately available or if there were casualties.
Security forces sealed off the area following the blast, the source said.
There has been no claim of responsibility for the attack.
Police officer shot dead
Meanwhile, a police officer was shot dead on Wednesday in Yemen's southern Shabwah province, a local official has said.
"Unidentified gunmen on a motorbike opened fire on a traffic officer in provincial capital Ataq, killing him instantly," the official, requesting anonymity, told The Anadolu Agency.
There has been no claim of responsibility, while the Yemeni authorities have yet to comment on the incident.
Yemen has been dogged by turmoil since pro-democracy protests forced autocratic president Ali Abdullah Saleh to step down in 2012 after 33 years in power.
In recent months, scores of security personnel have been killed in attacks in the country's south, for which officials point the finger at Al-Qaeda-linked militants.
Politically fractious Yemen has recently appeared on the verge of civil war, with members of the powerful Shiite Houthi group seeking to expand their influence beyond capital Sanaa, which they took control of in September.