Background: The early COVID-19 literature suggested that people with cancer may be more likely to be infected with SARS-CoV-2 or develop COVID-19 than people without cancer, due to increased health services contact and/or immunocompromise. While some studies were criticised due to small patient numbers and methodological limitations, they created or reinforced concerns of clinicians and people with cancer. These risks are also important in COVID-19 vaccine prioritisation decisions. We performed a systematic review to critically assess and summarise the early literature. Methods and findings: We conducted a systematic search of Medline/Embase/BioRxiv/MedRxiv/SSRN databases including peer-reviewed journal articles, letters/commentaries, and non-peer-reviewed pre-print articles for 1 January–1 July 2020. The primary endpoints were diagnosis of COVID-19 and positive SARS-CoV-2 test. We assessed risk of bias using a tool adapted from the Newcastle-Ottawa Scale. Twelve studies were included in the quantitative synthesis. All four studies of COVID-19 incidence (including 24,181,727 individuals, 125,649 with pre-existing cancer) reported that people with cancer had higher COVID-19 incidence rates. Eight studies reported SARS-CoV-2 test positivity for > 472,000 individuals, 48,370 with pre-existing cancer. Seven of these studies comparing people with any and without cancer, were pooled using random effects [pooled odds ratio 0.91, 95 %CI: 0.57–1.47; unadjusted for age, sex, or comorbidities]. Two studies suggested people with active or haematological cancer had lower risk of a positive test. All 12 studies had high risk of bias; none included universal or random COVID-19/SARS-CoV-2 testing. Conclusions: The early literature on susceptibility to SARS-CoV-2/COVID-19 for people with cancer is characterised by pervasive biases and limited data. To provide high-quality evidence to inform decision-making, studies of risk of SARS-CoV-2/COVID-19 for people with cancer should control for other potential modifiers of infection risk, including age, sex, comorbidities, exposure to the virus, protective measures taken, and vaccination, in addition to stratifying analyses by cancer type, stage at diagnosis, and treatment received.