Due to popular demand, you can now flip your Dota 2 HUD.
This allows players to view the mini map on the other side.
Step 1: Go to Settings (found on the upper right side of the Dota 2 client)
Step 2: Click Options
Step 3: Check "Draw Minimap on the Right"
You can now play DOTA 2 with the map on the reverse side!