The stability, electronic, and optical properties of single-walled carbon nanotubes (CNTs) and graphene non-covalently functionalized with free-base tetraphenylporphyrin (TPP) molecules is addressed by density functional theory calculations. We study the TPP physisorption on 42 CNT species, particularly those with chiral indices (n, m), where 5 <= n <= 12 and 0 <= m <= n. Our results show a quite strong pi-pi interaction between TPP and the CNT surface, with binding energies ranging from 1.1 to 1.8 eV, where higher energies can be associated with increasing CNT diameters. We also find that the TPP optical absorptions would not be affected by the CNT diameter or chirality. Results for the TPP physisorption on graphene show a remarkable stability with binding energy of 3.2 eV, inducing a small redshift on the pi-stacked TPP absorption bands. The strong graphene-TPP interaction also induces a charge transfer from TPP to graphene, indicating a n-type doping mechanism without compromising the graphene structure.