No fatalities were immediately reported but the building is staffed by soldiers at all hours and hospitals were placed on alert, AFP reported.
Footage on local media showed smoke rising from the entirely blackened multi-storey building.
The cause of the blaze, which broke out at the headquarters of the Ismailia Security Directorate before dawn, is not yet known.
Of 26 wounded who were transferred to a local hospital, 24 had suffered from “asphyxiation” and two from burns, local media reported citing the health ministry.
Twelve more were treated at the scene.
The health ministry deployed 50 ambulances to the scene, which were joined by military emergency services including two planes, according to state media.
Deadly fires are a common hazard in Egypt, where fire codes are rarely enforced and emergency services are often slow to arrive.
In August 2022, a fire caused by a short circuit killed 41 worshippers in a Cairo church, prompting calls to improve the country's infrastructure and the response time of the fire brigade.
In March 2021, at least 20 people died in a fire at a textile factory in the capital, while in 2020, two hospital fires killed 14 people.