A sample of 16 blue compact dwarf galaxies (BCDs) in the Virgo Cluster has been imaged in the near-infrared (NIR) in J and Ks on the 2.1 m telescope at the Observatorio Astronómico Nacional in the Sierra San Pedro Mártir in Mexico. Isophotes as faint as μJ=24 mag arcsec-2 and μKs=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 dwarf irregular galaxies (dIs), and a Gaussian component, which quantifies the starburst near the center. Isophotal and total fitted NIR magnitudes have been calculated, along with semimajor axes at μJ=23 mag arcsec-2 and μKs=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-Ks=0.7 and 0.9 mag. The diffuse component represents the overwhelming majority of the NIR light for most BCDs, with 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 center. The central burst correlates with the diffuse component, with brighter BCDs having stronger starbursts, suggesting that more massive objects are forming stars more efficiently. BCDs lie on the ``fundamental plane'' defined by dIs in Paper I, following the same relation between sech absolute magnitude, sech central surface brightness, and the hydrogen line width W20, although the scatter is larger than for the dIs. On the other hand, correlations between the sech absolute magnitude and the sech central surface brightness in Ks for BCDs and dIs are equally good, indicating that BCD line widths may be enhanced by turbulence or winds. These data were acquired at the Observatorio Astronómico Nacional in the Sierra San Pedro Mártir, Mexico.