Mikkelsen turned professional in 1979, and played only at the World Snooker Championship in his first three seasons. He lost in the first qualifying round each time; 7–9 to Roy Amdor in 1980, 4–9 to Jimmy White in 1981, and 6–9 to Colin Roscoe in 1982. After not competing during the 1982–83 snooker season, Mikkelsen reached the third qualifying round of the 1984 World Snooker Championship with wins over Paul Medati and Frank Jonik before being eliminated 3–10 by Willie Thorne. In a qualifying match for the 1985 World Snooker Championship, Mikkelsen compiled a break of 132, but lost 9–10 to Malcolm Bradley.