One doctor said a Tehran eye hospital had gone into crisis mode, while the BBC also obtained a message from a medic in another hospital saying it did not have enough surgeons to cope with the influx of patients.
On Friday, US President Donald Trump said Iran was in "big trouble" and warned "you better not start shooting because we'll start shooting too".
Iran in a letter to the UN Security Council blamed the US for turning the protests into what it called "violent subversive acts and widespread vandalism".
Anti-government protests, which continued on Friday, have taken place in dozens of locations, with two human rights groups reporting at least 50 protesters have been killed.
The BBC and most other international news organisations are barred from reporting inside Iran, and the country has been under a near-total internet blackout since Thursday evening, making obtaining and verifying information difficult.
A doctor from Iran, who contacted the BBC via Starlink satellite internet on Friday night, said Farabi Hospital, Tehran's main eye specialist centre, had gone into crisis mode, with emergency services overwhelmed.
Non-urgent admissions and surgeries were said to have been suspended, and staff called in to deal with emergency cases.
The BBC also obtained a video and audio message from a medic in a hospital in the south-west city of Shiraz on Thursday. The medic said large numbers of injured people were being brought in, and the hospital did not have enough surgeons to cope with the influx. He claimed many of the wounded had gunshot injuries to the head and eyes.
A health worker at another hospital in Tehran also told the BBC that their patients included gunshot wound victims.
