Mooney M20J pilot reported left main tire failure likely due to FOD on landing resulting in runway excursion. Aircraft came to stop and was towed to hangar.

Narrative

Runway Excursion After Tire Failure on Landing Roll -- Mooney M20JDuring the landing rollout in a Mooney; the aircraft suddenly pulled sharply to the left. I applied right rudder and regained runway alignment briefly; but the aircraft began pulling left again despite full right rudder and right brake application. The left main tire had failed; later determined to likely be caused by foreign object damage (FOD). The aircraft departed the left side of runway XX; and the left wing contacted a taxiway sign; resulting in skin damage.One passenger was on board; no injuries occurred. After the aircraft came to a stop; I secured it; notified airport operations; and coordinated for a tug to move it to the ramp/hangar area. Right wind from 030 10 gusting 15 was also a contributing factor. Tire failure during landing rollout; likely from FOD. Loss of directional control following tire failure.Suggestions: Review of directional control procedures and emergency response for landing gear/tire failures.