The blast at Sina At'har health centre caused damage to buildings in the vicinity and sent a plume of thick black smoke into the night sky, state television reported.
At least 19 people were killed after a powerful explosion hit a clinic in northern Tehran.
Last week, an explosion occurred close to a sensitive military site near Tehran which the defense ministry said was caused by a leaking tank at a gas storage facility. Mr Maleki added that firefighters had rescued 20 people. A nearby hospital went on alert to receive additional injured people if necessary.
The spokesman of the emergency services told Mehr news agency that "Twenty-five people were at the location when the explosion took place and ten men and three women died" and confirmed the hospitalization of six others.
State TV reported it was possible there could be more explosions because there are a number of oxygen capsules remaining in the medical center.
Left: Fire and smoke rise from the building, shown in footage recorded from a near-by building of the explosion in Tehran on June 30, 2020.
Witness Marjan Haghighi told The Associated Press that police blocked roads to the neighborhood.
Iran's state media quoted senior officials as saying the blast was caused by a gas leak.
Earlier in the day, media reports suggested that multiple explosions occurred near Tajrish square in the Iranian capital.
Parchin is a site suspected of having hosted conventional explosion tests applicable to nuclear power, which the country denies.