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A sample of 16 blue compact dwarf galaxies (BCDs) in the Virgo Cluster hasbeen imaged in the near-infrared (NIR) in $J$ and $K_s$ on the 2.1m telescopeat OAN-SPM in Mexico. Isophotes as faint as $\mu_J$ = 24 mag arcsec$^{-2}$ and$\mu_{K_s}$ = 23 mag arcsec$^{-2}$ have been reached in most of the targets.Surface brightness profiles can be fitted across the whole range of radii bythe sum of two components: a hyperbolic secant (sech) function, which is knownto fit the light profiles of dIs, and a Gaussian component, which quantifiesthe starburst near the centre. Isophotal and total fitted NIR magnitudes havebeen calculated, along with semimajor axes at $\mu_J$ = 23 mag arcsec$^{-2}$and $\mu_{K_s}$ = 22 mag arcsec$^{-2}$. The diffuse underlying component andthe young starburst have been quantified using the profile fitting. Most colorprofiles show a constant color, between $J-K_s$=0.7 to 0.9 mag. The diffusecomponent represents the overwhelming majority of the NIR light for most BCDs,the starburst enhancing the flux by less than about 0.3 mag. Linearcorrelations were found between the sech scale length and the sech magnitude,and between the sech semimajor axis and the sech magnitude. Overall, galaxieswith more luminous diffuse components are larger and brighter in the centre.The central burst correlates with the diffuse component, with brighter BCDshaving stronger star-bursts, suggesting that more massive objects are formingstars more efficiently. BCDs lie on the ``fundamental plane'' defined by dwarfirregulars (dISs) in Paper I, following the same relation between sech absolutemagnitude, sech central surface brightness, and the hydrogen line-width$W_{20}$, although the scatter is larger than for the dIs. [one sentence cut]Comment: Accepted in A

Infrared Properties of Star-forming Dwarf Galaxies. II. Blue Compact Dwarf Galaxies in the Virgo Cluster