I don't see anything in the Verilog-AMS LRM that would let you do this -- no %-code for Monte-Carlo run.  You could check with your vendor to see if they've added any extensions.

I noticed in one simulator's documentation that there are some %-codes that you can use on the command line, including one that can be used to replace quoted strings within the netlist.  It's a little round-about, then, to open a file using the name provided by a string parameter of your verilog-a module, the parameter would get set to a (quoted string) value in the netlist, and then you replace the quoted string with the command-line argument, and you have to hope that the command-line replacement allows you to specify the Monte-Carlo run number.