Curl is basically just an HTTP client, just like a browser. It can send HTTP requests to a given URL, and show the response body (the HTML) as raw text.
What you're asking is similar to saying, "can i prevent people using Firefox from sending requests to my site?"
If the request comes from a single IP then you can block it using IPTABLES (assuming you are running on linux). Other option as mentioned above is to block requests based on the user agent if that's unique.
If you have a public API and people are sending CURL requests, then the easiest way is to put it behind an authentication method, or only allow it from certain IP addresses.