We present fast methods for fitting sparse multivariate linear models to high-throughput data. We induce model sparsity using an L1 penalty and consider the case when the response matrix and the covariate matrices are large. Standard methods for estimation of these penalized regression models fail if the problem is converted to the corresponding univariate regression problem, motivating our fast estimation algorithms that utilize the structure of the model. We evaluate our method's performance on simulated data and two Arabidopsis genetic datasets with multivariate responses. Our algorithms have been implemented in the Julia programming language and are available.