The well has reached total depth of 2,738m within the Dunlin formation and will now be plugged and abandoned.
The Kalvklumpen well targeted sandstones of the Palaeocene Hermod formation and the Jurassic Brent Group.
Whilst excellent reservoirs were confirmed in both targets, no hydrocarbons were found, the company said.
Det Norske Oljeselskap undertook the drilling operation as operator, using the Songa Delta rig.
Faroe chief executive Graham Stewart said whilst the results for the Kavlklumpen well are disappointing, the extensive data acquired will now be applied to evaluate and de-risk further prospects within this and the adjacent licences held by Faroe in this prospective area.