By all means you can connect a ceiling fan directly to a dimmer switch but you may run into problems along the way.
Can you put a ceiling fan on a dimmer switch.
You can install a ceiling fan light dual dimmer switch to operate the fan speed and light intensity from the original wall switch location.
If your ceiling fan has wiring already in place where you have a separate switch for fan control then you can have the separate controls wired to independent switches.
A broken ceiling fan motor and a house fire are obviously not ideal outcomes however there is some good news.
A dimmer switch as the name suggests lets you control the intensity of the light produced from the light to which it is connected such as a ceiling fan with a built in lighting fixture.
You cannot use a dimmer switch on a fan motor but you can find fan speed controllers.
The wall dimmer switch reduces power flow and interferes with the fan control.
In this circumstance the light kit could be connected to a dimmer switch and the fan motor connected to a toggle switch.
You may need an electrician for this.