As the AD9833 has a minimum output voltage of 38mV and a maximum of 650mV, I was wondering if it's possible to program the AD9833 to change the minimum and maximum output voltage.
It is a fixed output voltage of 600mV peak to peak with the maximums you specified to allow for some variation. You can easily scale this to whatever level you need using an opamp. Keep in mind that the output of the AD9833 is fairly high impedance, so you will want to use a topology (like a non-inverting amplifier topology) where the output of the AD9833 is attached to a high impedance gate. If you want it to be programmatically controlled, you can adjust the feedback ratio on your op amp using a digipot (digital potentiometer).