She said in that case, she "went completely nuts" and chased the man off.
It was after telling the stories that Streep said the experiences changed her permanently.
Streep did not give any more details or name names, other than to say Cher witnessed the second incident and watched as she "went nuts".
"In one instance, I played dead and waited until the blows stopped, watching. People say you do, from about 50ft above, as I was beaten," she said. "In the second instance, someone else was being abused and i just went completely nuts and went after this man. Ask Cher, she was there."
"The thug ran away, it was a miracle," she said.
Streep and Cher worked together on the 1983 film Silkwood and have remained friends since.
Cher will also star in the 2018 musical comedy film, Mamma Mia! Here We Go Again, alongside Streep