The Christian leader made the comments as part of a campaign video to encourage more female Conservative candidates to get into Parliament.
She said her dad, who was a vicar, told her to ignore boundaries and to aim for the top.
"My father encouraged me to whatever job I did, just get on with it and do my best," she said.
"He always encouraged me to see no barriers, no boundaries, just go out there and do the best that you can and aim high."
The PM founded Women2Win ten years ago to boost the number of women who run for Conservative constituencies.
The latest video is urging fathers to speak to their daughters about taking on whatever career they want and fulfilling their potential to become an MP if they so wish.
Theresa May's father was killed in a car accident when she was 25, her mother died a year later.
Mrs May and her husband moved into No 10 in July after winning the Tory leadership contest after the European Union referendum and resignation of David Cameron.
She finished: "I think it is hugely important that young girls are able to see women in Parliament."
At present there are 68 Tory women among the 191 female MPs in the Commons.