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Removing outbursts from multiwavelength light curves of the blazar Mrk~421,we construct outburstless time series for this system. A model-independentpower spectrum light curve analysis in the optical, hard X-ray and gamma-raysfor this outburstless state and also the full light-curves, show clear evidencefor a periodicity of ~ 310 days across all wavelengths studied. A subsequentfull maximum likelihood analysis fitting an eclipse model confirms aperiodicity of 310 \pm 1 days. The power spectrum of the signal in theoutburstless state of the source does not follow a flicker noise behaviour andso, the system producing it is not self-organised. This and the fact that theperiodicity is better defined in the outburstless state, strongly suggests thatit is not produced by any internal physical processes associated to the centralengine. The simplest physical mechanism to which this periodicity could beascribed is a dynamical effect produced by an orbiting supermassive black holecompanion eclipsing the central engine. Interestingly, the optimal eclipsemodel infers a brightness enhancement of (136.4 \pm 20 )%, suggesting aneclipse resulting in a gravitational lensing brightening. Consisting with thisinterpretation, the eclipse occurs for only ( 9.7 \pm 0.2)% of the orbitalperiod.

An eclipsing binary black hole candidate system in the blazar Mrk 421