He was a co-owner of Moses & Søn G. Melchior, a trading house founded by his grandfather.

He was a member of the Maritime and Commercial Court (Sø- og Handelsretten) from 1883 to 1905 and of Grosserer-Societetet's committee from 1885 to 1904.

He was cashier for Foreningen til Søfartens Fremme and vice president of Komitéen for Dansk Vestindien, and chairman of Administrationen.

Melchior died on 25 November 1912 and is buried in the Jewish Northern Cemetery in Copenhagen.

An obelisk in the centre of the Kildevæld Quarter commemorates his role in the establishment of Arbejdernes Byggeforening.