Chairman Phil Holder will assume day to day responsibility for the business pending a replacement for Harrison.
The AIM-listed contractor is now starting its search for his successor.
Holder said: “I would like to thank Martin for his work with the company over the past five years.
“The board remains committed to helping the company deliver its strategy, and is confident that the senior management team will continue to develop and build the business.”
Three months ago, Fulcrum appointed Daren Harris, former concrete contractor Byrne Group director, as chief financial officer.
In the year to March, Fulcrum raised revenue 20% to nearly £50m generating a pretax profit of £6m.