Iran was among the first group of countries with a major outbreak of COVID-19 in Asia. With nearly 100 exported cases to various other countries by Feb 25, 2020 it has since been the epicentre of the outbreak in the Middle East. By examining the age- and gender-stratified national data taken from PCR-confirmed cases and deaths related to COVID-19 on Mar 13 (reported by the Iranian ministry of health) and those taken from hospitalised patients in 14 university hospitals across Tehran on Apr 4 (reported by Tehran University of Medical Sciences), we find that the crude case fatality ratio of the two reports in those aged 60 and younger are identical and are almost 10 times higher than those reported from China, Italy, Spain and several other European countries (reported from government or ministry of health websites). Assuming a constant attack rate across all age-groups, we adjust for demography, delay from confirmation to death, and under-ascertainment of cases, to estimate the infection fatality ratio based on the reports from Mar 13. We find that our estimates are aligned with reports from China and the UK for those aged 60 and above [n=4609], but are 2-3 times higher in younger age-groups [n=6756] suggesting that only less than 10% of symptomatic cases were detected across the country at the time. Using inbound travel data (from China to Iran) and matching the dates of the flights with prevalence of cases in China from Jan to Mar 2020, we assess the risk of importation of active cases into the country. Further, using outbound travel data, based on detected cases exported from Iran to several other countries, we estimate the size of the outbreak in the country on Feb 25 and Mar 6 to be 13,700 (95% CI: 7,600 - 33,300) and 60,500 (43,200 - 209,200), respectively. We next estimate the start of the outbreak using 18 whole-genome sequences obtained from cases with a travel history to Iran and the first sequence obtained from inside the country. Finally, we use a mathematical model to predict the evolution of the epidemic and assess its burden on the healthcare system. Our modelling analysis suggests the first peak of the epidemic was on Apr 5 and the next one likely follows within the next 6-10 weeks with approximately 30,000 ICU beds required (IQR: 12K - 60K) and over 1 million active cases (IQR: 740K - 3.7M) during the peak weeks. We caution that relaxed, stringent intervention measures, during a period of highly under-reported spread, would result in misinformed public health decisions and a significant burden on the hospitals in the coming weeks.