"We wish Margarita all the best. Send her our best wishes", Putin said at a SPIEF plenary meeting in St. Petersburg.
Simonyan, who is pregnant with her third child, was hospitalised overnight after a stressful run-in with a correspondent in Moscow who pressed her with questions about the Moscow mayor.
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The 39-year-old spent the night at the hospital, where she had fluids given to her intravenously. She posted a photo of her diagnosis, which said she had run the risk of a late miscarriage overstress.
Simonyan is the editor-in-chief of the Rossiya Segodnya news agency, which is a media partner of SPIEF, an economic forum attended every year by world and business leaders. Sputnik is a part of the agency.