Supernovae (SNe) exploding in a dense circumstellar medium (CSM) are hypothesized to accelerate cosmic rays in collisionless shocks and emit GeV gamma rays and TeV neutrinos on a time scale of several months. We perform the first systematic search for gamma-ray emission in Fermi LAT data in the energy range from 100 MeV to 300 GeV from the ensemble of 147 SNe Type IIn exploding in dense CSM. We search for a gamma-ray excess at each SNe location in a one year time window. In order to enhance a possible weak signal, we simultaneously study the closest and optically brightest sources of our sample in a joint-likelihood analysis in three different time windows (1 year, 6 months and 3 months). For the most promising source of the sample, SN 2010jl (PTF10aaxf), we repeat the analysis with an extended time window lasting 4.5 years. We do not find a significant excess in gamma rays for any individual source nor for the combined sources and provide model-independent flux upper limits for both cases. In addition, we derive limits on the gamma-ray luminosity and the ratio of gamma-ray-to-optical luminosity ratio as a function of the index of the proton injection spectrum assuming a generic gamma-ray production model. Furthermore, we present detailed flux predictions based on multi-wavelength observations and the corresponding flux upper limit at 95% confidence level (CL) for the source SN 2010jl (PTF10aaxf).