If the Preferences window is the active one you can use bpy.ops.wm.window_close()

Otherwise you have to overwrite the context.

With Blender 3.2 there was a change. Now we better use Context.temp_override(window, area, region, **keywords) for this.

The following example should work with all versions:

import bpy

bpy.ops.preferences.addon_show(module='io_scene_obj')   # example

for window in bpy.context.window_manager.windows:   # searching preference window
    screen = window.screen
    for area in screen.areas:
        if area.type == 'PREFERENCES':
    
            # Blender 3.2 and more
            if bpy.app.version[0] == 3 and bpy.app.version[1] > 1:      
                from bpy import context
                with context.temp_override(window=window, area=area):
                    bpy.ops.wm.window_close() 

            # Blender < 3.2 with override context            
            else:                                                       
                override = {'window': window, 'screen': screen, 'area': area}
                bpy.ops.wm.window_close(override)               

            break

If the Preferences window is the active one you can use bpy.ops.wm.window_close()

Otherwise you have to overwrite the context.

With Blender 3.2 there was a change. Now we better use Context.temp_override(window, area, region, **keywords) for this.

The following example should work with all versions:

edited: thanks to scurest

import bpy

bpy.ops.preferences.addon_show(module='io_scene_obj')   # example

for window in bpy.context.window_manager.windows:   # searching preference window
    screen = window.screen
    for area in screen.areas:
        if area.type == 'PREFERENCES':
    
            # Blender 3.2 and more
            if bpy.app.version >= (3, 2, 0):      
                from bpy import context
                with context.temp_override(window=window, area=area):
                    bpy.ops.wm.window_close() 

            # Blender < 3.2 with override context            
            else:                                                       
                override = {'window': window, 'screen': screen, 'area': area}
                bpy.ops.wm.window_close(override)               

            break