Recent years have witnessed the rise of misinformation campaigns that spread specific narratives on social media to manipulate public opinions on different areas, such as politics and healthcare. Consequently, an effective and efficient automatic methodology to estimate the influence of the misinformation on user beliefs and activities is needed. However, existing works on misinformation impact estimation either rely on small-scale psychological experiments or can only discover the correlation between user behaviour and misinformation. To address these issues, in this paper, we build up a causal framework that model the causal effect of misinformation from the perspective of temporal point process. To adapt the large-scale data, we design an efficient yet precise way to estimate the \textbf{Individual Treatment Effect} (ITE) via neural temporal point process and gaussian mixture models. Extensive experiments on synthetic dataset verify the effectiveness and efficiency of our model. We further apply our model on a real-world dataset of social media posts and engagements about COVID-19 vaccines. The experimental results indicate that our model recognized identifiable causal effect of misinformation that hurts people's subjective emotions toward the vaccines.