26-year-old Ekeng had come on as a substitute in the second half, and collapsed seven minutes into his appearance.
It was reported by Romanian media that the midfielder had suffered a heart attack.
Ekeng was taken to the local hospital, but medics were unable to revive him.
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The Cameroon FA confirmed his death.
Dinamo also confirmed it in a statement on their website, which read: "Dinamo lost tonight, forever, footballer Patrick Claude Ekeng. On behalf of everyone at Dinamo, sincere condolences to the bereaved family. God rest his soul."
Reports immediately afterwards suggested that although he received CPR for one and a half hours at the hospital, he received no first aid on the pitch, and that the ambulance at the stadium was not equipped for an emergency and was present just for transportation.
In 2000, the club's captain Catalin Hildan collapsed and died on the pitch during a friendly match.
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