With the steep rise in multimodal content on social media, multimodal sarcasm detection has gained widespread attention from research communities. Existing studies depend on large-scale data, which is challenging to obtain and expensive to annotate. Thus, investigating this problem in a few-shot scenario is required. Overtly complex multimodal models are prone to overfitting on in-domain data, which hampers their performance on out-of-distribution (OOD) data. To address these issues, we propose Continuous Attentive Multimodal Prompt Tuning model (CAMP), that leverages the prompt tuning paradigm to handle few-shot multimodal sarcasm detection. To overcome the siloed learning process of continuous prompt tokens, we design a novel, continuous multimodal attentive prompt where the continuous tokens intricately engage with both image and text tokens, enabling the assimilation of knowledge from different input modalities. Experimental results indicate that our method outperforms other multimodal baseline methods in the few-shot setting and OOD scenarios.