The firm, which turned over around £17m working for retail chains like Lidl and the Co-op on contracts of around £2m, was set up 13 years ago.
Johnson Construction had been struggling for several years and posted a £1.5m loss in 2013 before restructuring the business and returning a small profit of £353,000.
Russell Cash and Ben Woolrych of FRP Advisory are handling the administration and have laid off 16 of the 20 staff.
The administration relates solely to Johnson Construction UK and other associate or group companies continue to operate as normal.
FRP Advisory said: “Circumstances were such that activity levels had reduced significantly in 2015.
“After an evaluation of the company’s financial position, the joint administrators have regrettably made staff redundant. Four staff members have been retained in the short term to assist the joint administrators.
“Efforts are currently being concentrated on evaluating the position with regards to work in progress and completed work to ensure recoveries are maximised.”