Humans show language-biased image recognition for a word-embedded image, known as picture-word interference. Such interference depends on hierarchical semantic categories and reflects that human language processing highly interacts with visual processing. Similar to humans, recent artificial models jointly trained on texts and images, e.g., OpenAI CLIP, show language-biased image classification. Exploring whether the bias leads to interference similar to those observed in humans can contribute to understanding how much the model acquires hierarchical semantic representations from joint learning of language and vision. The present study introduces methodological tools from the cognitive science literature to assess the biases of artificial models. Specifically, we introduce a benchmark task to test whether words superimposed on images can distort the image classification across different category levels and, if it can, whether the perturbation is due to the shared semantic representation between language and vision. Our dataset is a set of word-embedded images and consists of a mixture of natural image datasets and hierarchical word labels with superordinate/basic category levels. Using this benchmark test, we evaluate the CLIP model. We show that presenting words distorts the image classification by the model across different category levels, but the effect does not depend on the semantic relationship between images and embedded words. This suggests that the semantic word representation in the CLIP visual processing is not shared with the image representation, although the word representation strongly dominates for word-embedded images.