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 timescale of several months. We perform the first systematic search for {gamma}-ray emission in Fermi Large Area Telescope data in the energy range from 100MeV to 300GeV from the ensemble of 147 SNe Type IIn exploding in a 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 (PTF 10aaxf), 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 a 95% confidence level (CL) for the source SN 2010jl (PTF 10aaxf).