Although the game will be best played with a more powerful system, a modest single-core setup will suffice.
Posting over on On-Mirrors-Edge.com, DICE's Fredrik Thylander has confirmed the minimum PC specifications needed to run Mirror's Edge. While you won't be able to run the title with fancy graphical effects and PhysX support, the game should be playable on a modest rig.
Mirror's Edge minimum system requirements:
Operating System: Microsoft Windows XP SP2/Vista
Processor: Intel Pentium 4 3.0GHz or 100% compatible equivalent
Memory: 1GB RAM
Video Card: 256MB memory with Shader Model 3.0
HDD Space: 8GB
DVD Drive: 1x DVD Drive
Soundcard: Soundcard with DirectX 9.0c compatibility
DirectX: DirectX 9.0c
Network: An online connection is required for access to Leaderboards
Mirror's Edge is out now for Xbox 360 and PS3 and is scheduled for a PC release on January 16, 2009.