While hydraulic fracturing is widely used to enhance the permeability of deep geothermal, gas and oil reservoirs, it remains challenging to infer the heterogeneous distribution of permeability in the fractured zone. Typically, a limited number of boreholes are available at which reservoir imaging and tracer testing can be conducted. The number of observations is often far fewer than the number of estimable permeabilities, making model inversion ill-posed. To overcome this problem, this study combined the autoencoder neural network (a deep learning approach) with Bayesian inversion algorithm (using Markov Chain Monte Carlo, MCMC sampling) to estimate permeability in the enhanced geothermal reservoir, based on a single-well-injection-withdrawal test (SWIW). The autoencoder neural network was used to reduce parameter dimensionality into low-dimension codes by four orders of magnitude, while MCMC sampling was used to update the low-dimension codes according to the SWIW observations. The spatial distribution of permeability was then reconstructed from these low-dimension codes using the original autoencoder neural network. Application of the approach to a synthetic enhanced geothermal system demonstrated that the methodology achieved rapid stabilization of the Bayesian inversion. When the root mean square error (RMSE) between modelled and observed borehole temperature and flow rate values was less than unity, estimated permeability values were comparable to the synthetic reference case, with a mean square error lower than 0.001 mD. The combination of the deep-learning based dimension reduction technique and Bayesian inversion algorithm allow the estimate of permeability distribution in deep artificial reservoirs based on limited number of boreholes.