Background: COVID-19-driven pandemic has caused panic, fear, and stress among all strata of society. The study aimed to assess stress and the factors that influence it in a representative population in the state of Tamil Nadu (TN)—a state in the southern India where the levels of stress have not been measured yet. Methods: From April 13 to April 25, 2020, we conducted an online survey among the TN population using the snowball sampling technique, collecting basic demographic data. COVID-19-perceived stress was collected through COVID-19 Peritraumatic Distress Index (CPDI). Binomial regression analysis was used to identify the extent of the relationship between CPDI and sociodemographic factors by estimating the odds of having significant stress. P ≤ 0.05 was considered significant. Results: A total of 2,317 valid responses were received. Of the respondents, 830 (35.82%) were males, 1,084 (46.79%) were below 25 years of age, and 2,297 (99.14%) were native residents of TN. The mean(±SD) CPDI was 20.66±12.03. While 1,830 (77.2%) respondents had low or no stress, 478 (20.2%) had mild to moderate stress, and 63 (2.7%) had severe stress. The bivariate model included marital status, age, nativity, and income. The odds of having significant stress (mild–moderate or severe) for a 25–34 year age group as compared to >55 years group was 2.38 (P < 0.001). As compared to widowed, the married had higher odds ratio (3.41, P = 0.05). Compared to those with >10 lakh annual income, those with 2.5–5 lakhs annual income had odds ratio of 1.65 (95% CI = 1.01 to 2.7, P = 0.05). Conclusions: During the lockdown due to COVID-19, every 1 in 5 TN population had some form of stress, as measured by CPDI. Our model identified certain factors driving the stress, which would help policy framers to initiate an appropriate response.