"We urge those involved in the fighting to give the wounded on all sides immediate and safe access to the medical treatment they need," Ramy Saliba, the ICRC's regional director, said in a statement.
Saliba said some of the fighting in the southwest city of Sabha has taken place near an area hospital. Parties to the conflict must ensure health facilities are protected from violence "at all times," he said.
Georg Charpentier, U.N. deputy envoy to Libya, issued a similar appeal Sunday.
The Libyan government in early January declared a state of emergency for southern parts of the country and Charpentier said there was a general lack of food and medicine in the region because of the fighting.
The ICRC said "scores" of people have been killed or injured in the region since fighting erupted mid-January.
"Essential supplies are not getting through owing to the volatile security situation that has forced airports to close," Saliba said. "There are already fuel and gas shortages, and food supplies are running out."
Libyan authorities have struggled to restore national order since civil war ended in 2011.