Air carrier Captain reported descending below the MSA while on approach resulting in flight towards terrain and ATC issuing an advisory. The flight crew corrected their altitude and course and landed safely at the airport.

Narrative

While on a night visual approach to ZZZ; I accidentally and momentarily went below MSA in the ZZZ terminal area in order to avoid inbound weather and keep the airport environment in sight. After ATC notified us; I made a turn away from the hazards and towards the final approach course to prepare the aircraft for intercepting the final and configuring the aircraft for landing. At no point was there a GPWS warning or any other notifications regarding the accidental deviation.Cause - Due to an inbound thunderstorm cell; I elected to accept the visual approach to Runway XX at ZZZ. However; to maintain the airport environment in sight I momentarily descended below MSA until Tower informed us that we were below the MSA. After confirming our position; I elected to make a turn for the final approach course; away from any hazards; in order to maintain the airport in sight and set the aircraft up for its final approach and landing.Suggestions - When in doubt; just ask for ATC control and vectors to final in order to maintain the safest course. Although MSA was briefed during the approach brief; when in the terminal area review it again to ensure you know exactly where it is.