Enke started to play football at "BSG Jenapharm Jena", a local club in his city. In 1985 he came to the youth teams of Jena's major football club, Carl Zeiss Jena. On 11 November 1995, at the age of 18, he had his first professional match for Jena in the German 2. Bundesliga. In 1996, he came to Borussia Mönchengladbach in the German Bundesliga.