A (local) population of about ten thousand people should be enough. In my opinion there are three factors here.
1. Is there enough need for a restaurant? There seem to be around 14.000 McDonalds restaurants in the US, which is roughly one per 23.000 inhabitants. Assuming that the first one on Mars will be on the smaller size and have less competition, 10.000 potential customers should be fine.
2. Can you produce the menu items? I think this is the easiest point. Most of the ingredients derived from plants will be fine, something like lettuce, grains and tomatoes will be among the first things grown on Mars anyway. Meat will be harder since raising cattle would cost more of the limited available labour and greenhouse-space than it would to directly grow crops, but lab-grown meat is definitely no further in the future than large self-sufficient martian colonies. And since the colony needs to eat, the food will have to be there anyway. Interestingly, the only problem I see is the packaging. 121
Large amounts of trash are most likely a no-go on a small colony and neither the wood for paper nor the oil for most common plastics will be easily accessible on Mars.
3. Are you allowed to do this? Actually I think this is the critical point. Depending on your vision of the future, martian colonies will either be state funded military/science/vanity missions, or research/mining/vanity operations bankrolled by large companies and conglomerates. This means that initially all colonists in a location will be permanently bound to an employer and critical resources like food, water and energy will be centrally controlled. You'll have to wait quite a while and most likely a few generations for "free martian citizens" and an internal free market to develop. The more likely option is outside involvement. Just think of the publicity of being the first interplanetary fast-food chain. So the most likely thing is that some company executives on earth will just cut a deal and some company/state-run cafeteria on Mars will be rebranded into the first McDonalds in space.
Edit: Another point mentioned in the comments is the economy of scale. It is true that they will not be able to keep their cheap earth prices for food, but neither can anybody else. Most likely the colony's food production will be centralized at this stage anyway and the martians food will either payed for by the colony's owner or the colonists will just expect that food is a lot more expensive. 207