Foden has 24 goals for City in all competitions this season and has often been utilised in more central roles by coach Pep Guardiola
Costa was ruled out of the tournament in the US on Friday after scans revealed a torn muscle in his left thigh, Brazil's football confederation said, reports Xinhua.
The 34-year-old currently plays for US Major League Soccer club Orlando City, where he has scored 11 goals in 32 matches since March last year.
Costa's absence is another blow to Brazil, who are already without Barcelona star Neymar after the Catalan club said the forward would not be released for both the Copa America and the Olympic Games in August.
Brazil will debut in the Copa America against Ecuador in Pasadena on Jun 4.