There are many fruits that have a high acidity level and can cause heartburn, though cherries are not one of them.
This fruit has a relatively low acidity rating of 4.0, which means that it is okay for those who have problems with acid reflux to eat regularly. Those who have this problem should stay away from eating fruits like oranges, because they contain quite a bit of acid and can worsen pre-existing heartburn.
Not many foods have the ability to cause heartburn itself, though there are some that can exacerbate the condition. Anyone who has problems with acid reflux should avoid fruits with high acidity ratings.