The star's mother gave birth to Gracie in June, and the new addition to the family has made her realise the importance of being a good "role model".
She told E! News: "Gracie is five months old, she's adorable. I'm obsessed with her and becoming a big sister.
"I know I've had the responsibility to be a role model for girls but, when you have a little sister of your own, you kind of think, 'OK, this is legit.' "
The 21-year-old singer also revealed she has plans to return to acting as a career once she's completed her Stars Dance tour - and she's enjoying the freedom of seeing the world.
She added:"It's my first world tour, so actually being able to experience these places while I'm there alone, all by myself, it's great.
"I feel like a big girl ... I'm going take some time for myself and get back into movies."
Being independent has become important for Gomez who - despite the birth of her sister - made the decision to move out of her parents' home earlier this year.
She previously said: "Yeah, you know I think it's time. I didn't ever want to be forceful to saying, 'OK, I've made enough to get my own house and OK, let's blow it off and do whatever.'
"I just love being with my family and I love knowing that they're there. But yeah, I think it's probably time for me to get my own house."