The number of patients attending emergency departments and minor injury units in Swansea Bay has plummeted by nearly 50% in recent weeks.
Reductions in admissions have been reported across the UK as fewer people appear to be suffering accidents while staying at home.
Many people are also worried about going to hospital because Covid-19 cases are being treated there.
In addition, hospitals have suspended non-urgent activity, although emergency surgery and some cancer treatments continue, among others.
Leaders at Swansea Bay University Health Board considered a number of reports at a meeting behind closed doors on April 30, which focused on the coronavirus response.
A risk management report cited the astonishing drop in emergency department and minor injury unit attendance at Morriston Hospital, Singleton Hospital and Neath Port Talbot Hospital over the last three weeks.
But an increase in future health needs has been added to the health board's risk register, along with the financial implications of responding to the pandemic.
Speaking last week, Morriston Hospital emergency department consultant Andy MacNab said the number of cases of heart attacks and mini-strokes - often the precursor to a full-blown stroke - were lower than expected.
"That's the thing that's worrying us," he said.
Dr MacNab urged people who were "properly ill" to get to their nearest emergency department.
Managers are recalibrating some of the health board's existing risks in response to the all-out focus on Covid-19.
More patients who were due to have things like hip and knee surgery are now breaching 36-week and 52-week threshold waiting times, while surgical cancer activity is being affected by the availability of critical care beds.
Nurse numbers, added the report, were at times falling below minimum levels because nurses were self-isolating or ill. Action has been taken to address this, such as bringing retired and student nurses on stream.
The health board has taken major steps to prepare for coronavirus in a short space of time, increasing capacity and commissioning field hospitals at the Llandarcy Academy of Sport and Bay Studios.
The risk report said management, self-governance and transparency was vital at a time when scrutiny from external bodies, like Healthcare Inspectorate Wales, was at its lowest.
It said: "These risks need to be crucially considered and included into the health board's response to recovery from the Covid-19 pandemic."
The health board, which covers Swansea and Neath Port Talbot, finished the 2019-20 financial year £16.2 million in deficit, partly because an extra £5.4 million had to be found to resolve issues linked to when Bridgend left the health board area last April to join Cwm Taf Morgannwg University Health Board.
The health board tweeted from Thursday's meeting, paying respects to members of staff who had died since the outbreak, and praising "the incredible work" of all of its teams.
Speaking on Radio Wales on May 1, head of NHS Wales, Andrew Goodall, said emergency departments were still operating at "surge capacity" but that the outlook had improved, thanks to the public obeying the current restrictions and reducing the spread of Covid-19.
But he said he remained concerned about other peaks throughout this year.
Dr Goodall also said he was concerned about the drop-off in emergency department admissions in Wales.
Take part in our Great British Lockdown Survey below:
"We are ready to treat them," he said.
Dr Goodall said discussions had been taking place with health boards and clinician groups about re-starting more routine activity, although he stressed it had to be done carefully.
"It will be a few steps forward," he said.
