We present Infrared Space Observatory (ISO) observations of 16OH and 18OH toward Sgr B2 with a spectral resolution of 35 km/s. The OH J=5/2-3/2 and J=3/2-1/2 rotational lines of the 2Pi1/2 ladder are seen in emission while the cross-ladder transitions (from the 2Pi3/2 J=3/2 to the J=1/2, 3/2 and 5/2 levels of the 2Pi1/2ladder), and the 2Pi3/2 J=5/2-3/2 and J=7/2-5/2 lines are detected in absorption. The 18OH 2Pi3/2 J=5/2-3/2 Lambda-doublet at 120 mu is also observed in absorption. All OH Lambda-doublets are resolved (except the 98 mu) and show, in addition to the strong absorption at the velocity of Sgr B2, several velocity components associated to the gas surrounding Sgr B2 and to the foreground clouds along the line of sight. No asymmetries in the line intensities of each doublet have been observed. We have modeled the observations using a non-local radiative transfer code and found that the OH absorption/emission must arise in a shell around Sgr B2 not resolved by the ISO/LWS beam. The gas density is moderate, with upper limits of 10^4 cm^{-3} and 300 K in temperature. The OH abundance is high,(2-5)10^{-6}. We argue that a widespread photon dominated region explains the enhancement of OH abundance.Peer reviewed