Background It is unclear how people with hypertension are responding to the COVID-19 pandemic given their increased risk, and whether targeted public health strategies are needed. Objective This retrospective case-control study compared people with hypertension to matched healthy controls during the COVID-19 lockdown to determine whether they have higher risk perceptions, anxiety, and vaccination intentions. Methods Baseline data from a national survey were collected in April 2020 during the COVID-19 lockdown in Australia. People who reported hypertension with no other chronic conditions were randomly matched to healthy controls of similar age, gender, education, and health literacy level. A subset including participants with hypertension was followed up at 2 months after restrictions were eased. Risk perceptions, anxiety, and vaccination intentions were measured in April and June. Results Of the 4362 baseline participants, 466 (10.7%) reported hypertension with no other chronic conditions. A subset of 1369 people were followed up at 2 months, which included 147 (10.7%) participants with hypertension. At baseline, perceived seriousness was high for both hypertension and control groups. The hypertension group reported greater anxiety compared to the controls and were more willing to vaccinate against influenza, but COVID-19 vaccination intentions were similar. At follow-up, these differences were no longer present in the longitudinal subsample. Perceived seriousness and anxiety had decreased, but vaccination intentions for both influenza and COVID-19 remained high across groups (>80%). Conclusions Anxiety was above normal levels during the COVID-19 lockdown. It was higher in the hypertension group, which also had higher vaccination intentions. Groups that are more vulnerable to COVID-19 may require targeted mental health screening during periods of greater risk. Despite a decrease in perceived risk and anxiety after 2 months of lockdown restrictions, vaccination intentions remained high, which is encouraging for the future prevention of COVID-19.