The driver of the concrete mixer was killed and five other people were injured.
According to the preliminary version, the accident occurred due to the failure of the brakes of a loaded truck.
A source at the embassy said the life and health of the staff of the Russian Embassy in Tehran were not in danger.
"We confirm the information. There are no victims among the embassy staff. The accident occurred at 4:40 a.m., local time," the embassy said.
At the site of the damaged wall, the municipal authorities have erected a temporary shield, establishing an additional post for diplomatic police, the embassy added.
Policemen, paramedics and firefighters are working at the scene.