Baah featured for Ghana U20 at the 2015 U20 African Cup of Nations, playing an important role in the match for the 3rd/4th place by stopping a penalty. Baah subsequently also received a call up for the 2015 FIFA U-20 World Cup, assuming the role of reserve goalkeeper for Ghana U20. Kwame featured in all four qualifier games played by Ghana U20 in the qualifiers for 2017 U20 African Cup of Nations.