About 20-40% of cancer patients develop brain metastases, causing significant morbidity and mortality. Stereotactic radiation treatment is an established option that delivers high dose radiation to the target while sparing the surrounding normal tissue. However, up to 20% of metastatic brain tumours progress despite stereotactic treatment, and it can take months before it is evident on follow-up imaging. An early predictor of radiation therapy outcome in terms of tumour local failure (LF) is crucial, and can facilitate treatment adjustments or allow for early salvage treatment. In this study, an MR-based radiomics framework was proposed to derive and investigate quantitative MRI (qMRI) biomarkers for the outcome of LF in brain metastasis patients treated with hypo-fractionated stereotactic radiation therapy (SRT). The qMRI biomarkers were constructed through a multi-step feature extraction/reduction/selection framework using the conventional MR imaging data acquired from 100 patients (133 lesions), and were applied in conjunction with machine learning techniques for outcome prediction and risk assessment. The results indicated that the majority of the features in the optimal qMRI biomarkers characterize the heterogeneity in the surrounding regions of tumour including edema and tumour/lesion margins. The optimal qMRI biomarker consisted of five features that predict the outcome of LF with an area under the curve (AUC) of 0.79, and a cross-validated sensitivity and specificity of 81% and 79%, respectively. The Kaplan-Meier analyses showed a statistically significant difference in local control (p-value < 0.0001) and overall survival (p = 0.01). Findings from this study are a step towards using qMRI for early prediction of local failure in brain metastasis patients treated with SRT. This may facilitate early adjustments in treatment, such as surgical resection or salvage radiation, that can potentially improve treatment outcomes. Investigations on larger cohorts of patients are, however, required for further validation of the technique.