Fun fact: it seems camels emit less methane than cows or sheep.
You could make it so that your alien camel produces more methane rather than less. Let's say it produces as much as a cow, between 70 and 120kg / Earth year.
The alien camel could route that methane into a special organ, where symbiotic bacteria would oxidize it anaerobically. If your camel can also produce or eat nitrates, they can get three water molecules for every methane molecule. Otherwise they are capped at one H2O molecule per methane molecule.
The relevant reactions are:
(That's a total of 12 molecules of water of output for four molecules of methane in the input).
That raises a whole can of worms about how the chemistry of those beings would be, but hey, if sci-fi will take giant worms that swim through sand and beings that can harvest sunlight from orbit, then sci-fi can take a camel with a water plant on its back.
Now, as for how much water that generates, let's do a rule of three. The atomic weight of hydrogen, carbon and oxygen, rounded to integers, are 1, 12 and 16, respectively. So:
$$\frac{H_2O}{CH_4} = \frac{18}{16} = 1.125$$
$$\frac{3H_2O}{CH_4} = \frac{54}{16} = 3.375$$
So for every kilogram of methane, your alien camel can produce either 1.125 kg of water or 3.375 kg, depending on how they can metabolize it.
Now, to see if that is enough, I did some quick googling and found this:
Camels can go up to seven months in the desert without drinking water. During such a time, they may lose nearly half of their body weight.(...) Very thirsty camels can drink up to 100 liters of water during a single visit to the well. (...)
Camels are just very efficient at using water, and they’re well-adapted for dehydration.
100L of water for ~215 days means a camel needs 465 mL of water a day, on average.
If your alien camel produces as much methane as a cow, and can metabolize with nitrates, they could produce 70kg of methane a year, which would lead to 236.25 kg of water (which equals 236.25 liters in ideal conditions, gotta love the metric system). That's 647mL a day, more than enough to keep your alien camel going! The extra margin could be used comfortably for other activities besides its basal metabolism.
If your camel cannot use nitrates, then it will generate about 216mL of water per day. That's half what it needs. It will not be self-sufficient, but it will only need to drink half the amount of water it would need otherwise. In a desert environment where water is hard to come by, this may be a very positive adaptation.