Born in Cottbus, Melzig began his career with Energie Cottbus, helping the club earn promotion to the DDR-Oberliga in 1986, and again in 1988 after they had bounced straight back down to the DDR-Liga. After German reunification, Cottbus failed to qualify for the professional leagues, so in 1991 Melzig joined Dynamo Dresden, who had entered the Bundesliga. He was a first-team regular in two seasons with Dynamo, before joining Bayer Leverkusen for another two-year spell, in which he was mostly used as a backup.