But rather than answering the question directly, she simply replied: "Have a good day."
Jenner subsequently addressed the issue on her Twitter account in a bid to clarify her stance.
She wrote on the micro-blogging platform: "I didn't expect to get asked this on my Saturday morning coffee run, but I'm clear about where I stand.
"It's an issue of fairness and we need to protect girls' sports in our schools."
Meanwhile, Arnold Schwarzenegger recently gave his view on Jenner's decision to run to become the governor of California.
The Hollywood star - who served as the governor between 2003 and 2011 - urged the reality star to outline a "clear vision" for the state.
He said: "The key thing about all of this is, it doesn't matter if it's Caitlyn or it's anyone else. Do you have a clear vision where you want to go? What are the kind of changes you want to make, and why are you qualified to become governor?
"That's what you have to convince the people."