A flexible display module and a flexible display device are disclosed. The flexible display module includes a flexible display panel, a circuit board, and a display panel protective structure. The flexible display panel includes an effective display portion and a bonding portion. The display panel protective structure is located one a rear of the effective display portion. An indentation is defined in a side of the display panel protective structure away from the effective display portion. The bonding portion is disposed in the indentation and is electrically connected to the effective display portion, and the circuit board is disposed in the indentation and is electrically connected to the bonding portion.