By default, Maya will be set up to use the latest version of FBX, but you can switch to earlier versions in the FBX export settings. To do so, you need to edit the export preset:
With the asset you want to export selected, open the Export options (click on the square next to Export Selection... to get to the options window):
I had to restart Maya after doing this to get it to actually switch versions, but your mileage may vary.
In the Export Selection Options, set the File Type to FBX Export.
Then, under File Type Specific Options, select Edit Preset:
In the preset, scroll down until you see Advanced Options. Expand this and click on FBX File Format. In here, you can set the FBX version you need to use. Save the preset.