The intermediate-mass star Beta Pictoris is known to be surrounded by a structured edge-on debris disk within which a gas giant planet was discovered orbiting at 8-10 AU. The physical properties of Beta Pic b were previously inferred from broad and narrow-band 0.9-4.8 microns photometry. We used commissioning data of the Gemini Planet Imager (GPI) to obtain new astrometry and a low-resolution (R=35-39) J-band (1.12-1.35 microns) spectrum of the planet. We find that the planet has passed the quadrature. We constrain its semi-major axis to $leq$ 10 AU (90 % prob.) with a peak at 8.9+0.4-0.6 AU. The joint fit of the planet astrometry and the most recent radial velocity measurements of the star yields a planets dynamical mass $leq$ 20 MJup (greater than 96 % prob.). The extracted spectrum of Beta Pic b is similar to those of young L1-1.5+1 dwarfs. We use the spectral type estimate to revise the planet luminosity to log(L/Lsun)=-3.90+-0.07. The 0.9-4.8 microns photometry and spectrum are reproduced for Teff=1650+-150 K and a log g lower than 4.7 dex by 12 grids of PHOENIX-based and LESIA atmospheric models. If we adopt the most recent system age estimate (21+-4 Myr), the bolometric luminosity and the constraints on the dynamical mass of Beta Pic b are only reproduced by warm- and hot-start tracks with initial entropies Si greater than 10.5 kB/baryon. Such initial conditions may result from an inefficient accretion shock and/or a planetesimal density at formation higher than in the classical core accretion model. Considering a younger age for the system or a conservative formation time for Beta Pic b does not change these conclusions.
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