B737-800 Captain reported that after gate arrival ramp personnel advised him the #1 engine was on fire. The reporter activated the fire bottle and the fire went out.

Narrative

After parking and while doing the shutdown checklist; there was a loud banging on the nose of the aircraft. Looking outside I saw the rampers waving their arms and signaling us. I opened the side window; and they were yelling that my number 1 engine was on fire. I had no indications of a fire in the flightdeck. I pulled the number 1 fire handle and rotated it to fire the fire bottle. The rampers told me the fire went out immediately. I then opened the flight deck door and told the number 1 flight attendant what happened and that I wanted everybody off the plane. The gate agent had parked the jet bridge but heard fire and left without opening the cabin door. I looked out the flight deck window and saw the jet bridge was in the correct position so I told the number 1 Flight Attendant to open the door so we could get everybody off the plane. Maintenance had met the plane for other minor cabin issues when we were parking. Since I had visual confirmation that the fire was out and a number of people already looking at the engine and another fire bottle; I decided not to make a PA to the passengers. I did not want to start a panic and have people get hurt. Everybody deplaned without incident or injury.The aircraft had returned to the gate on a previous flight because of flames being reported coming out of #1 engine. Maintenance checked it and found nothing wrong.