Statistical sub-pixel detection via the adaptive matched filter (AMF) has been shown to improve the molecular imaging sensitivity and specificity of optoacoustic (photoacoustic) imaging. Applied to multispectral optoacoustic tomography (MSOT), AMF assumes that the spatially-varying tissue spectra follow a multivariate Gaussian distribution, that the spectrum of the target molecule is precisely known and that the molecular target lies in "low probability" within the data. However, when these assumptions are violated, AMF may result in considerable performance degradation. The objective of this work is to develop a robust statistical detection framework that is appropriately suited to the characteristics of MSOT molecular imaging. Using experimental imaging data, we perform a statistical characterization of MSOT tissue images and conclude to a detector that is based on the t-distribution. More importantly, we introduce a method for estimating the covariance matrix of the background-tissue statistical distribution, which enables robust detection performance independently of the molecular target size or intensity. The performance of the statistical detection framework is assessed through simulations and experimental in vivo measurements and compared to previously used methods.