Feeblemind has a duration of instantaneous. However, it also produces an ongoing effect, and the spell's text describes when this effect ends (emphasis added):
At the end of every 30 days, the creature can repeat its saving throw against this spell. If it succeeds on its saving throw, the spell ends.
The spell can also be ended by greater restoration, heal, or wish.
The fact that the text refers to the spell ending, as opposed to just "the effect" or something similar, implies that it produces an ongoing magical spell effect, which can be dispelled using Dispel Magic. However, it has also been argued that any effects that persist beyond a spell's stated duration cannot be considered magical (with the classic example being fires started by a Fireball spell). Applying this rule to Feeblemind, it shouldn't have any ongoing effects since its duration is instantaneous. So, which is it? Are the ongoing effects of Feeblemind considered magical and therefore susceptible to effects like Dispel Magic, or are are they simply the lingering result of the initial shattering of the creature's intellect and personality?
(Note that the final sentence quoted above does not by itself rule out Dispel Magic and other ways of ending the spell. It gives additional options for ending the spell, but it doesn't say these are the only options.)
Feeblemind can't be dispelled
The feeblemind spell has an instantaneous duration which means specifically:
This is supported by designer intent in a (now unofficial) pair of tweets by Jeremy Crawford, and has been addressed in the Sage Advice Compendium:
(that answer also continues with the examples of animate dead and cure wounds)
The most likely fix to the ambiguity would to rephrase (or interpret) the later clauses to 'the spell's effect ends'. The game does not always make a distinction between the two terms. Specifically the spell Leomund's secret chest (in the SRD as secret chest) is also instantaneous and includes the paragraph (emphasis mine):
Here both ending the spell's effect and ending the spell are used to describe the same thing, which is similar to that of feeblemind. Likely if the effect of feeblemind was to be dispellable it's duration would have been listed as 'Until Dispelled' or something similar, like with transmute rock or magic jar.