Background: Social media chatter in 2020 has been largely dominated by the COVID-19 pandemic. Existing research shows that COVID-19 discourse is highly politicized, with political preferences linked to beliefs and disbeliefs about the virus. As it happens with topics that become politicized, people may fall into echo chambers, which is the idea that one is only presented with information they already agree with, thereby reinforcing one's confirmation bias. Understanding the relationship between information dissemination and political preference is crucial for effective public health communication. Objective: We aimed to study the extent of polarization and examine the structure of echo chambers related to COVID-19 discourse on Twitter in the United States. Methods: First, we presented Retweet-BERT, a scalable and highly accurate model for estimating user polarity by leveraging language features and network structures. Then, by analyzing the user polarity predicted by Retweet-BERT, we provided new insights into the characterization of partisan users. Results: We observed that right-leaning users were noticeably more vocal and active in the production and consumption of COVID-19 information. We also found that most of the highly influential users were partisan, which may contribute to further polarization. Importantly, while echo chambers exist in both the right- and left-leaning communities, the right-leaning community was by far more densely connected within their echo chamber and isolated from the rest. Conclusions: We provided empirical evidence that political echo chambers are prevalent, especially in the right-leaning community, which can exacerbate the exposure to information in line with pre-existing users' views. Our findings have broader implications in developing effective public health campaigns and promoting the circulation of factual information online.