Object search is a challenging task because when given complex language descriptions (e.g., "find the white cup on the table"), the robot must move its camera through the environment and recognize the described object. Previous works map language descriptions to a set of fixed object detectors with predetermined noise models, but these approaches are challenging to scale because new detectors need to be made for each object. In this work, we bridge the gap in realistic object search by posing the search problem as a partially observable Markov decision process (POMDP) where the object detector and visual sensor noise in the observation model is determined by a single Deep Neural Network conditioned on complex language descriptions. We incorporate the neural network's outputs into our language-conditioned observation model (LCOM) to represent dynamically changing sensor noise. With an LCOM, any language description of an object can be used to generate an appropriate object detector and noise model, and training an LCOM only requires readily available supervised image-caption datasets. We empirically evaluate our method by comparing against a state-of-the-art object search algorithm in simulation, and demonstrate that planning with our observation model yields a significantly higher average task completion rate (from 0.46 to 0.66) and more efficient and quicker object search than with a fixed-noise model. We demonstrate our method on a Boston Dynamics Spot robot, enabling it to handle complex natural language object descriptions and efficiently find objects in a room-scale environment.