A sample of 16 blue compact dwarf galaxies (BCDs) in the Virgo Cluster has been imaged in the near-infrared (NIR) in J and K_s on the 2.1m telescope at OAN-SPM in Mexico. Isophotes as faint as μ_J = 24 mag arcsec^-2 and μ_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 by the sum of two components: a hyperbolic secant (sech) function, which is known to fit the light profiles of dIs, and a Gaussian

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... t, which quantifies the starburst near the centre. Isophotal and total fitted NIR magnitudes have been calculated, along with semimajor axes at μ_J = 23 mag arcsec^-2 and μ_K_s = 22 mag arcsec^-2. The diffuse underlying component and the young starburst have been quantified using the profile fitting. Most color profiles show a constant color, between J-K_s=0.7 to 0.9 mag. The diffuse component represents the overwhelming majority of the NIR light for most BCDs, the starburst enhancing the flux by less than about 0.3 mag. Linear correlations were found between the sech scale length and the sech magnitude, and between the sech semimajor axis and the sech magnitude. Overall, galaxies with more luminous diffuse components are larger and brighter in the centre. The central burst correlates with the diffuse component, with brighter BCDs having stronger star-bursts, suggesting that more massive objects are forming stars more efficiently. BCDs lie on the "fundamental plane" defined by dwarf irregulars (dISs) in Paper I, following the same relation between sech absolute magnitude, sech central surface brightness, and the hydrogen line-width W_20, although the scatter is larger than for the dIs. [one sentence cut]