City ambulance service chief Gulnara Sydykova said the 130-meter building had been fully evacuated and that one woman suffered from smoke inhalation and two firefighters were slightly injured by falling glass.
The fire was put out in about two hours, said the building's manager, Svyatoslav Nogai.
The fire appeared to have started on a 27th-floor balcony, but its cause had not been established, the Kazakhstan Today news agency reported, citing Emergencies Minister Shalbay Kulmakhan, who was at the scene.
The blaze broke out around 4 p.m. in the building housing the Transportation, Information and Industry ministries and other government agencies, and spread downward, reaching the middle floors, officials and witnesses at the site said.
Berik Bekzhanov, an Information Ministry official who was working on the 29th floor when the fire broke out, said that fire alarms failed to go off.
Bolatbek Bilalov, a building security official, said internal phone lines were used to alert and evacuate the 2,000 people working in the building.
A Message from The Moscow Times:
Dear readers,
We are facing unprecedented challenges. Russia's Prosecutor General's Office has designated The Moscow Times as an "undesirable" organization, criminalizing our work and putting our staff at risk of prosecution. This follows our earlier unjust labeling as a "foreign agent."
These actions are direct attempts to silence independent journalism in Russia. The authorities claim our work "discredits the decisions of the Russian leadership." We see things differently: we strive to provide accurate, unbiased reporting on Russia.
We, the journalists of The Moscow Times, refuse to be silenced. But to continue our work, we need your help.
Your support, no matter how small, makes a world of difference. If you can, please support us monthly starting from just $2. It's quick to set up, and every contribution makes a significant impact.
By supporting The Moscow Times, you're defending open, independent journalism in the face of repression. Thank you for standing with us.

Remind me later.