Background: The SARS-CoV-2 pandemic has become an enormous worldwide challenge over the last two years. However, little is still known about the risk of Long COVID (LC) in patients without comorbidities. Thus, we aimed to assess the predictors of LC in patients without comorbidities. Methods: Patients’ information, the course of the disease with symptoms, and post-COVID-19 complaints were collected within 4–12 weeks after COVID-19 recovery. Next, the patients were followed for at least 3 months. ECG, 24-h ECG monitoring, 24-h blood pressure (BP) monitoring, echocardiography, and selected biochemical tests were performed. LC was recognized based on the WHO definition. Results: We identified 701 consecutive patients, 488 of whom completed a 3-month follow-up (63% women). Comparisons were made between the LC group (n = 218) and patients without any symptoms after SARS-CoV-2 recovery (non-LC group) (n = 270). Patients with a severe course of acute-phase COVID-19 developed LC complications more often (34% vs. 19%, p < 0.0001). The persistent symptoms were observed in 45% of LC patients. The LC group also had significantly more symptoms during the acute phase of COVID-19, and they suffered significantly more often from dyspnoea (48 vs. 33%), fatigue (72 vs. 63%), chest pain (50 vs. 36%), leg muscle pain (41 vs. 32%), headache (66 vs. 52%), arthralgia (44 vs. 25%), and chills (34 vs. 25%). In LC patients, significant differences regarding sex and body mass index were observed—woman: 69% vs. 56% (p = 0.003), and BMI: 28 [24–31] vs. 26 kg/m2 [23–30] (p < 0.001), respectively. The number of symptoms in the acute phase was significantly greater in the LC group than in the control group (5 [2–8] vs. 2 [1–5], p = 0.0001). The LC group also had a higher 24-h heart rate (77 [72–83] vs. 75 [70–81], p = 0.021) at admission to the outpatient clinic. Multivariate regression analysis showed that LC patients had a higher BMI (odds ratio (OR): 1.06, 95% confidence intervals [CI]: 1.02–1.10, p = 0.007), almost twice as often had a severe course of COVID-19 (OR: 1.74, CI: 1.07–2.81, p = 0.025), and presented with joint pain in the acute phase (OR: 1.90, CI: 1.23–2.95, p = 0.004). Conclusions: A severe course of COVID-19, BMI, and arthralgia are independently associated with the risk of Long COVID in healthy individuals.