For variables to be accessed through the mask, they need to be Simulink parameters. As you cannot have a "table" type in a Simulink parameter, the closest method is to convert your table into a "struct".
A "struct" will not include your row names, but will still include the column names.
To do this, create a mask over your MATLAB Function block.
The mask should have an "edit" parameter to specify the table object you are working with. You would also most likely want a "button" action to allow for a "uigetfile" callback to have a user select a file, then load the table as a mask parameter.
The "edit" parameter needs to hold the table value. On the mask initialization callback, set a variable using the "table2struct" function on your table parameter.
In the MATLAB function block, select Simulink from the top ribbon, then "Edit Data". Add a parameter with the same name as the mask structure parameter. You should now have access to a structure in the MATLAB function block.