Adapter modules have emerged as a general parameter-efficient means to specialize a pretrained encoder to new domains. Massively multilingual transformers (MMTs) have particularly benefited from additional training of language-specific adapters. However, this approach is not viable for the vast majority of languages, due to limitations in their corpus size or compute budgets. In this work, we propose MAD-G (Multilingual ADapter Generation), which contextually generates language adapters from language representations based on typological features. In contrast to prior work, our time- and space-efficient MAD-G approach enables (1) sharing of linguistic knowledge across languages and (2) zero-shot inference by generating language adapters for unseen languages. We thoroughly evaluate MAD-G in zero-shot cross-lingual transfer on part-of-speech tagging, dependency parsing, and named entity recognition. While offering (1) improved fine-tuning efficiency (by a factor of around 50 in our experiments), (2) a smaller parameter budget, and (3) increased language coverage, MAD-G remains competitive with more expensive methods for language-specific adapter training across the board. Moreover, it offers substantial benefits for low-resource languages, particularly on the NER task in low-resource African languages. Finally, we demonstrate that MAD-G's transfer performance can be further improved via: (i) multi-source training, i.e., by generating and combining adapters of multiple languages with available task-specific training data; and (ii) by further fine-tuning generated MAD-G adapters for languages with monolingual data.