The aircraft was operating as a scheduled flight from Karachi, Pakistan to Dubai, UAE with the Captain as the pilot flying (PF). The crew reported nothing unusual for the take-off at Karachi and the aircraft operated to Dubai without event. The incident occurred after landing on Dubai runway 12L, when the aircraft was taxiing along taxiway "X" to the passenger terminal. The aircraft was operated in a dedicated passenger configuration as flight PK 213 and the radio call-sign was "Pakistan 213". At 2349 hours local time, an Airport Safety Patrol member (Mobile 5) saw smoke and then a fire on the right landing gear of PK 213 and he immediately advised both the ATC Tower and the fire services. The marshaller at parking bay B7 blocked the area and also advised the fire services. The fire services arrived within 90 seconds and extinguished the fire. Upon notification from ATC, the Captain shut down the engines. He was advised that the fire had been extinguished so he did not evacuate the passengers. Once mobile steps had been positioned next to the aircraft, the passengers left the aircraft without incident.