The 18-times Romanian champions said that the 51-year-old was taken to Floreasca Hospital in an ambulance and is able to communicate.
"Doctors said that Eugen Neagoe's condition is stable at the moment," Dinamo said in a statement.
Local media reported that the first words spoken by Neagoe to the doctors at the hospital were: "What's the score?".
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Dinamo were beaten 2-0 at home to remain winless after the first two rounds of matches.
Former striker Neagoe has been repeatedly criticised by Dinamo's hardcore fans, known as 'ultras', since taking over last month. The supporters want him to quit as they were against the sacking of crowd favourite Mircea Rednic.
According to reports in Romanian media, Neagoe "couldn't eat for two days, drank loads of coffees and smoked like crazy" due to the criticism from the fans.
"We were very close to a tragedy," Dinamo chairman and former Romania keeper Florin Prunea said. "I can't understand the level of hate at this club. I can't believe it! It's just impossible, this can explode!"
Dinamo's Cameroon international Patrick Ekeng had died after collapsing on the pitch during the league match against Viitorul in 2016.
An inquiry into Ekeng's death revealed that the ambulance company that took him to hospital had faulty equipment and medicine beyond its expiry date in some of its vehicles.
Dinamo are one of the two most successful teams in Romania alongside city rivals FCSB, formerly known as Steaua Bucharest.
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