Beam search decoding is the de-facto method for decoding auto-regressive Neural Machine Translation (NMT) models, including multilingual NMT where the target language is specified as an input. However, decoding multilingual NMT models commonly produces ``off-target'' translations -- yielding translation outputs not in the intended language. In this paper, we first conduct an error analysis of off-target translations for a strong multilingual NMT model and identify how these decodings are produced during beam search. We then propose Language-informed Beam Search (LiBS), a general decoding algorithm incorporating an off-the-shelf Language Identification (LiD) model into beam search decoding to reduce off-target translations. LiBS is an inference-time procedure that is NMT-model agnostic and does not require any additional parallel data. Results show that our proposed LiBS algorithm on average improves +1.1 BLEU and +0.9 BLEU on WMT and OPUS datasets, and reduces off-target rates from 22.9\% to 7.7\% and 65.8\% to 25.3\% respectively.