CRJ-700 Flight crew reported Low Altitude Alert from ATC while on approach.

Narrative

ATC issued a low altitude alert while intercepting the final approach course to Runway XX into ZZZ. The alert was giving while descending to the altitude that ATC had assigned an we read back. What we heard was to fly direct ZZZZZ on the RNAV XX and cross ZZZZZ at 4;700FT then cleared for the approach. We read back those instructions. At 5;100FT and approximately 3 miles from ZZZZZ ATC issued a low altitude alert; a climb to 5;400FT and a heading off the approach. They then vectored us back to ZZZZZ to cross at 5;400FT and re-cleared us for the approach. The rest of the approach was uneventful. At no point did we get a terrain alert from our systems. We were in VMC (Airport was IMC with rain over the field) conditions and no terrain of obstacles were present. Event happened while doing OE (Operating Experience) with the FO. Cause: Likely due to a busy frequency. ATC gave us an instruction and we read back what we heard. Then ATC immediately started talking with another aircraft. I was confident in the instructions as they matched up with the approach charts and we could see that there was no immediate danger of terrain.