They suffered the injuries during France's 2-0 victory over Ukraine in the World Cup qualifiers in Poland on Friday.
Doue was replaced by Dembele at half-time, only for the 28-year-old to later limp off in the 81st minute.
Dembele, one of the favourites to win this year's Ballon d'Or, was instrumental in PSG's treble-winning campaign last season, which included their first Champions League title, Ligue 1, French Cup and French Super Cup triumphs.
He bagged 35 goals and registered 16 assists in 53 appearances across all competitions for PSG last season.
"Ousmane Dembele has suffered a serious injury to his right hamstring. He is expected to be unavailable for around six weeks," PSG said in a statement on Saturday.
"Also picking up an injury during the encounter, Desire Doue suffered a strain in his right calf and will be out for around four weeks."
PSG will next be in action when they host Lens in Ligue 1 on September 14th, followed by the start of their Champions League title defence against Atalanta three days later.
Their packed September schedule also includes Ligue 1 matches against Olympique de Marseille and Auxerre, leading up to a highly anticipated Champions League clash with Barcelona, Dembele's former club, on October 1st.
France, meanwhile, host Iceland in Group D of their World Cup qualifiers on Tuesday.