B737 Next Generation Undifferentiated
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 85; Flight Crew Total 3687; Flight Crew Type 3687
Communication Breakdown
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Provided Assistance; Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Environment - Non Weather Related; Human Factors
Flight was deviating off the ZZZZZ arrival due to thunderstorm activity. Subsequently cleared direct ZZZZZ and told to descend to 5;000 feet. While it is possible both the Captain and FO (First Officer) heard the wrong altitude; the FO read back 5;000 feet. Even though the published altitude is 6;000 feet; this did not seem unusual to us as we were flying below storm overhangs and had barely flown any of the arrival up to this point.  After reaching 5;000; the controller asked why we were at 5;000. We informed him that was our cleared altitude. He informed us 6;000 was the minimum vectoring altitude.
On arriving into ZZZ; we were taken off the ZZZZZ4 arrival due to thunderstorms in the terminal area. Upon contact with Terminal Radar Control we were issued radar vectors. The Air Traffic Controller stated that we would rejoin the arrival at ZZZZZ. We were told to fly heading 090 and cleared to descend from 9;000 to 6;000. The clearance was read back and confirmed by both of us. Shortly thereafter the controller gave us a further descent down to 5;000. The clearance was read back and confirmed by both of us. After the clearance was read back; ATC never intervened on the altitude that we read back. ATC then told us to fly direct to ZZZZZ. Whilst we were level at ZZZZZ at 5;000; ATC stated that [the next fix] had an altitude of 6;000 ft. I stated that we were cleared by him down to 5;000. There were no traffic conflicts.
Flight crew reported descending 1000 feet below minimum altitude on approach as cleared by ATC.