Knowledge representation is increasingly recognized as an effective method for information extraction. Nevertheless, numerous studies have disregarded its potential applications in the zero-shot setting. In this article, a novel framework, called knowledge-based prompt tuning for zero-shot relation triplet extraction (KBPT), was developed, founded on external ontology knowledge. This framework serves as a catalyst for exploring relation triplet extraction (RTE) methods within low-resource scenarios, warranting further scrutiny. Zero-shot setting RTE aims to extract multiple triplets that consist of head entities, tail entities, and relation labels from an input sentence, where the extracted relation labels are those that do not exist in the training set. To address the data scarcity problem in zero-shot RTE, a technique was introduced to synthesize training samples by prompting language models to generate structured texts. Specifically, this involves integrating language model prompts with structured text methodologies to create a structured prompt template. This template draws upon relation labels and ontology knowledge to generate synthetic training examples. The incorporation of external ontological knowledge enriches the semantic representation within the prompt template, enhancing its effectiveness. Further, a multiple triplets decoding (MTD) algorithm was developed to overcome the challenge of extracting multiple relation triplets from a sentence. To bridge the gap between knowledge and text, a collective training method was established to jointly optimize embedding representations. The proposed model is model-agnostic and can be applied to various PLMs. Exhaustive experiments on four public datasets with zero-shot settings were conducted to demonstrate the effectiveness of the proposed method. Compared to the baseline models, KBPT demonstrated enhancements of up to 14.65% and 24.19% in F1 score on the Wiki-ZSL and TACRED-Revisit datasets, respectively. Moreover, the proposed model achieved better performance compared with the current state-of-the-art (SOTA) model in terms of F1 score, precision-recall (P-R) curves and AUC. The code is available at https://Github.com/Phevos75/KBPT.