We report a femtosecond midinfrared study of the broadband low-energy response of individually separated (6,5) and (7,5) single-walled carbon nanotubes. Strong photoinduced absorption is observed around 200 meV, whose transition energy, oscillator strength, resonant chirality enhancement, and dynamics manifest the observation of quasi-one-dimensional intraexcitonic transitions. A model of the nanotube 1s-2p cross section agrees well with the signal amplitudes. Our study further reveals saturation of the photoinduced absorption with increasing phase-space filling of the correlated e-h pairs.