A variety of algorithms have been developed to identify jets originating from $b$-quark hadronization within the ATLAS experiment at the Large Hadron Collider. We describe the measurement of the false positive rate of the algorithm most commonly used in the LHC Run~2 ATLAS analyses, i.e. the misidentification rate of jets containing no $b$- nor $c$-hadrons. The measurement is based on the full data sample collected at a centre-of-mass energy of ${\sqrt{s} =}$ 13 TeV by the ATLAS detector during the year 2015 and 2016 and is performed in various ranges of jet transverse momenta and pseudorapidities. The final data sample used to extract the results is enriched in jets originating from light-flavour quark and gluon hadronization with the application of a dedicated algorithm reversing some of the criteria used in the nominal identification algorithm. The results are compared to the false positive rate predicted by the nominal ATLAS simulation in order to calibrate them.