In a personal interview with blog Humans of New York, she said she was told at the admissions exam she should forfeit her place so a man would not be drafted and sent to Vietnam.
She also revealed that as a young woman she learned to "control her emotions".
The Democratic candidate was criticised this week by the Republican party chairman for not smiling enough.
Reince Priebus was accused of sexism when he said Mrs Clinton had appeared to be defensive and angry when she was questioned by veterans at an event in New York on Wednesday.
Her Republican rival Donald Trump has also criticised her looks, saying he does not "look presidential" enough.
How do you 'look presidential'?
On the Humans of New York Facebook page, Mrs Clinton said she felt pressured into not going through with the law school exam.
"My friend and I were some of the only women in the room. I was feeling nervous. I was a senior in college. I wasn't sure how well I'd do. And while we're waiting for the exam to start, a group of men began to yell things like: 'You don't need to be here.' And 'There's plenty else you can do.' It turned into a real 'pile on.' One of them even said: 'If you take my spot, I'll get drafted, and I'll go to Vietnam, and I'll die.' And they weren't kidding around. It was intense. It got very personal."
She said that she can sometimes be perceived as "cold or unemotional" but she had learned to control her emotions when she was younger.
"That's a hard path to walk. Because you need to protect yourself, you need to keep steady, but at the same time you don't want to seem 'walled off.'"
Hillary Clinton has said she was singled out as one of the only women applying to go to Harvard law school.