The attacker had blinded security guards with a potent spray to force his way into the building before targeting Tatiana Felgengauer.
The man was arrested by police. According to the editor in chief, Alexei Venediktov, the injuries are not life-threatening.
An Israeli citizen who identified himself as Boris Grits confessed to stabbing Tatiana Felgenhauer in the neck at the radio station's Moscow office earlier in the day.
He posted photographs of police detaining a man, apparently the attacker, and of spots of blood on the floor.
Russian media later said two assailants had entered the building, but only one managed to get to the radio station's office.
He said the man has been detained.
Another station employee Vitaly Ruvinsky posted on Twitter a photo of the disheveled man dressed in a black jacket and pants.
Ms Felgenhauer is best known for co-hosting a popular morning show.
She is also actively involved in opposition rallies and has thousands of followers on her public Facebook page.
The broadcaster is owned by a media holding controlled by state-owned gas giant Gazprom but it does give air time to staunch critics of the Kremlin and its allies.
Ekho journalists have been attacked before, and liberal journalists are frequently equated with traitors in Russian Federation.
Dmitry Muratov, editor-in-chief of the Novaya Gazeta newspaper, says the failure of Russian authorities to respond to the recurrent attacks and threats against independent journalists, activists and opposition leaders have made such attacks possible.
The television report included photographs of Felgenhauer and audio of her complaining about conditions for journalists in Russian Federation.
Yulia Latynina, a veteran political analyst for the radio station who reports on the Kremlin and Russian security services, fled Russia last month after unknown assailants set fire to her vehicle.
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