Aminu Tsanyawa, the commissioner for health, confirmed the outbreak on Thursday.
The Nigeria Centre for Disease Control and Prevention (NCDC) has also announced new cases of the infection.
According to the agency, it is responding to reports of diphtheria cases in Lagos and Kano States and is monitoring the situation in Osun and Yobe States where cases are now being picked up.
In a statement on Friday, the Agency said in addition to clinically suspected cases, there have been laboratory-confirmed cases.
Calling for vigilance and maintenance of a high index of suspicion for diphtheria symptoms by health workers, the NCDC urges parents to ensure that their children are fully vaccinated against diphtheria as recommended in the childhood immunisation schedule.
It confirmed that the Agency is working with State Ministries of Health and partners to enhance surveillance and response to the outbreak while informing the public to stay safe at home and in their communities.
Diphtheria is a serious bacterial infection caused by the bacterium Corynebacterium species that affects the nose, throat and sometimes, skin of an individual.
It is a contagious disease transmitted easily between people through direct contact with infected people or contaminated clothing and objects, and droplets from coughing or sneezing.
People most at risk of contracting diphtheria include children and adults who have not received any or a single dose of the pentavalent vaccine (a diphtheria toxoid-containing vaccine).
Others are those who live in a crowded environment, areas with poor sanitation, healthcare workers and others who are exposed to suspected/confirmed cases of diphtheria.
They include fever, runny nose, sore throat, cough, red eyes (conjunctivitis), and neck swelling.
In severe cases, a thick grey or white patch appears on the tonsils and/or at the back of the throat associated with difficulty breathing.
The disease is preventable through immunization as recommended by the Nigeria childhood immunisation schedule of three doses of pentavalent vaccine (diphtheria toxoid-containing vaccine) for children in the 6th-, 10th- and 14th -week of life.
Also, Individuals with signs and symptoms suggestive of diphtheria should isolate themselves and notify the local government area, state disease surveillance officer (DSNO), or the NCDC through the toll-free line (6232).
Close contacts with a confirmed case of diphtheria should be closely monitored given antibiotics prophylaxis and started on diphtheria antitoxin treatment when indicated, the Agency noted.