Private ambulance owners launched the strike on Tuesday, demanding parking facilities inside the hospital premises.
The shutdown has left patients requiring transfers to other hospitals and families trying to take deceased relatives home in severe distress.
Many have waited for hours without finding an ambulance, forcing some to use alternative vehicles.
Ambulance owners say they have been forced to park on nearby roads since parking facilities inside the hospital were discontinued, exposing them to traffic congestion and fines.
They have vowed to continue the strike until their parking demand is addressed.
However, Dhaka Medical College Hospital Director Brigadier General AKM Farhad Hossain said there was no scope for permanent parking for private ambulances inside the hospital due to space constraints.
He said the authorities were taking steps to reduce congestion and improve discipline on the hospital premises.