One of Tigray’s main hospitals in the regional capital Mekelle is running out of body bags, the International Committee for the Red Cross said on Monday.
Local hospitals are also dangerously low on medical supplies, it said.
About 80 per cent of the wounded in the Ayder Referral Hospital, which the ICRC visited, are suffering from trauma injuries.
"The hospital is also lacking in body bags for the deceased. Food supplies are also low, affecting particularly those recovering from surgery and requiring specific nutritional needs," said Maria Soledad, the ICRC's head of operations in Ethiopia.
Sutures, antibodies, anticoagulants, painkillers and even basic supplies like gloves are also scarce.
The influx of injured comes more than three weeks after supply chains into Mekelle were disrupted.
"We need to ensure that health workers have the supplies and conditions they need to carry out their life-saving work,” Ms Soledad said.
While more than 44,000 refugees fled into Sudan, more Eritreans are coming into Mekelle from surrounding areas.
The UN on Sunday said that it had heard reports of violence and abductions among refugees in Tigray but that it was unable to confirm the claims.
UN high refugee commissioner Filippo Grandi said he hopes the “situation will develop in the next few days”.
“The situation in Mekelle today is quiet and we hope that we will be able to get urgently needed assistance here soon,” Ms Soledad said. “The staff at Ayder Referral Hospital are doing what they can with extremely limited resources, but they urgently need support.”
Ethiopia’s federal forces said they are also tracking down dissidents.
Armed individuals are entering Sudan and are being told to hand over their weapons before being separated from civilian refugee camps, the UN said.
Last month, Prime Minister Abiy Ahmed said his forces had regained control of Mekelle after weeks of fighting with the Tigray People’s Liberation Front.
In response, the TPLF said it would continue to fight the invaders until the last second and that the conflict was about the group’s “right to self-determination”.