By the time they reach early adulthood, English speakers are familiar with the meaning of thousands of words. In the last decades, computational simulations known as distributional semantic models (DSMs) have demonstrated that it is possible to induce word meaning representations solely from word co‐occurrence statistics extracted from a large amount of text. However, while these models learn in batch mode from large corpora, human word learning proceeds incrementally after minimal exposure to new words. In this study, we run a set of experiments investigating whether minimal distributional evidence from very short passages suffices to trigger successful word learning in subjects, testing their linguistic and visual intuitions about the concepts associated with new words. After confirming that subjects are indeed very efficient distributional learners even from small amounts of evidence, we test a DSM on the same multimodal task, finding that it behaves in a remarkable human‐like way. We conclude that DSMs provide a convincing computational account of word learning even at the early stages in which a word is first encountered, and the way they build meaning representations can offer new insights into human language acquisition.