Researchers at the University of Oxford looked at the health records of more than 230,000 COVID-19 patients, mostly from the US.
More than a third (34%) of COVID survivors were diagnosed with a neurological or psychiatric condition within half a year of being infected.
For 13% of people it was their first recorded neurological or psychiatric diagnosis, researchers found.
And the worse the coronavirus infection, the more likely patients were to suffer such a condition.
A neurological or psychiatric diagnosis occurred in 39% of those who were admitted to hospital, 46% of those in intensive care, and 62% in those who had encephalopathy - described as "delirium and other altered mental states" - during their COVID-19 infection.
Given the scale of the coronavirus pandemic and chronic nature of some neurological and psychiatric diagnoses, the study's authors concluded that "substantial effects on health and social care systems are likely to occur".
They argued that "urgent" research was needed to understand how and why such disorders occur and how they can be treated.
Researchers also found that overall there was a 44% greater risk of neurological and mental health diagnoses after COVID-19 than after flu, and a 16% greater risk after COVID-19 than with other respiratory tract infections such as pneumonia.
Paul Harrison, Professor of Psychiatry at the University of Oxford and the study's lead author, said: "These are real-world data from a large number of patients.
"They confirm the high rates of psychiatric diagnoses after COVID-19, and show that serious disorders affecting the nervous system (such as stroke and dementia) occur too.
"While the latter are much rarer, they are significant, especially in those who had severe COVID-19.
"Although the individual risks for most disorders are small, the effect across the whole population may be substantial for health and social care systems due to the scale of the pandemic and that many of these conditions are chronic.
"As a result, health care systems need to be resourced to deal with the anticipated need, both within primary and secondary care services."
The stress of knowing one has had COVID, and all the implications that go with that, contributes to the number of disorders, "rather than it being a direct effect, for example, of the virus on the brain, or the immune response to the virus on the brain," Mr Harrison told journalists on Tuesday.
For the peer-reviewed observational study, researchers looked at the incidence of 14 neurological and mental health disorders among 236,379 patients over the age of 10 who were infected with COVID-19 on or after 20 January 2020 and who were still alive on 13 December that year.