An embedded semiconductor die package is made by mounting a frame carrier to a temporary carrier with an adhesive. The frame carrier includes die mounting sites each having a lead frame interconnect structure around a cavity. A semiconductor die is disposed in each cavity. An encapsulant is deposited in the cavity over the die. A package interconnect structure is formed over the lead frame interconnect structure and encapsulant. The package interconnect structure and lead frame interconnect structure are electrically connected to the die. The frame carrier is singulated into individual embedded die packages. The semiconductor die can be vertically stacked or placed side-by-side within the cavity. The embedded die packages can be stacked and electrically interconnected through the lead frame interconnect structure. A semiconductor device can be mounted to the embedded die package and electrically connected to the die through the lead frame interconnect structure.