In principle, present-day spectroscopic technology could detect the "red edge" of chlorophyll if an extrasolar planet hosts vegetation that functions similar to life on Earth. However, spectroscopic telescopes are currently limited in their resolution and have the easiest time taking spectra for large Juipter-like planets. This limit is slowly dropping, though, and the next generation of telescopes, such as JWST, will hopefully be able to observe such spectra for Earth-sized planets.
This article from Astrobiology Magazine may be of interest:
What Does the Next Generation Telescope Need to Detect Life?