An air carrier pilot on a night time visual approach reported they received a low altitude alert from ATC.

Narrative

Approaching from the east; passing 5000 feet descending in night VMC conditions; Cascade Approach pointed out EUG. We called the field in sight and were subsequently cleared for a Visual Approach; then handed off to Eugene Tower and cleared to land. We selected 2000 ft. for MACTA; the FAF for Runway 16R and continued our descent. I had the city of Eugene and the field in sight; and believed I had adequate terrain clearance for the descent. At approximately 3800 ft. ATC issued a low altitude alert. Their transmission was somewhat garbled; so we asked for clarification; the alert was for us. I arrested the descent at approximately 3500 ft. increased power to maintain airspeed; and began to climb. We did not trigger any warnings or alerts from the Enhanced Ground Proximity Warning System (EGPWS) or Ground Proximity Warning System (GPWS). The very small amount of terrain displayed on the Navigation Display (ND) was green under the aircraft and yellow to our immediate right. We worked with ATC to confirm that we had cleared the terrain; then continued our descent to an uneventful landing.