You need to know if your SD module (link, please?) is 5V compatible or not.
I say this because many SD card adapters work at 3v3 signals only, so if your SD module has a level shifter it's ok using it with a 5V Arduino. Although many people say that it may work without level shifter, it probably worked first and then suddenly stopped when connected to the Mega (meaning it's probably gone).
So, double check the specifications to see if the module allows you to use it with 5V, and if in doubt test it back with UNO and see if it's still alive (hope so).
EDIT: I see someone made a modification/hack to the module, by adding a couple of diodes: