There are some fruits* that cause a peculiar (unpleasant) numb sensation in the mouth. An unripe persimmon or a quince are two examples that come to mind. I can't describe the feeling any more eloquently so my bet/hope is that you will know what feeling I am talking about.
Is there a word in English that describes the mentioned quality of these fruits and/or the sensation in the mouth?
*I don't know that only fruit can cause it, but I can't think of anything else at the moment.
Astringency or Puckering
From Wikipedia
Some foods, such as unripe fruits, contain tannins or calcium oxalate that cause an astringent or puckering sensation of the mucous membrane of the mouth. Examples include tea, red wine, rhubarb, and unripe persimmons and bananas.
Less exact terms for the astringent sensation are "dry", "rough", "harsh" (especially for wine), "tart" (normally referring to sourness), "rubbery", "hard" or "styptic"
From Education.com (emphasis mine):
Unripe persimmons are inedible because of the tannins that are diffused throughout the fruit. This tannins cause proteins in the saliva and tongue to coagulate. This coagulation of proteins produces the puckery, furry taste in the mouth that we refer to as astringency. This also happens with unripe bananas, some red wine and tea.
Desensitization generic term
The effect of certain chemicals such as capsaicin (active component of chili peppers; capsicum) on possible suppression of the sense of taste has been studied and it has been found that oral capsaicin reduces certain but not all taste sensations. There doesn't seem to be a specific name to such desensitization of the taste buds.
Certain foods (e.g. fats/ proteins) may leave a waxy residue on the tongue, also causing a suppression of the taste buds.
It's called hypogeusia - a diminished acuteness of the sense of taste. Related to this is dysgeusia - impaired or abnormal taste sensation. Although these conditions are caused by disease processes, temporary disturbances in taste can be caused by certain naturally occurring ingredients (by interfering with the normal functioning of taste receptors).
A less commonly used term is parageusia - the most familiar example of which is metallic taste from certain medications. Cacogeusia on the other hand is a hallucination or illusion of unpleasant taste, as seen in epilepsy.
Correction: Cacogeusia is now applied more generically to include real perception of bad taste. Example: the transient cacogeusia resulting from some varieties of pine nuts: http://www.sciencedirect.com/science/article/pii/S0266435612000101
The suggested term astringency is misleading. It is a generic term like numbness, not specific to taste in the mouth, strictly speaking not a sensation and certainly has no connotations of a numb sensation. You have astringent skin lotions for example.
I've always called it "setting one's teeth on edge".
Literally, to cause an unpleasant tingling of the teeth. More generally, the expression is used to describe any feeling of unpleasant distaste.
[The Phrase Finder]
I am not sure that this is exactly what you are describing, but it sounds like paresthesia
a sensation of tingling, tickling, prickling, pricking, or burning of a person's skin with no apparent long-term physical effect. The manifestation of a paresthesia may be transient or chronic.
Some of these sensations are commonly called pins and needles.
There is also an allergic reaction in the mouth called oral allergy syndrome (OAS) characterized by
an itching or burning sensation in the lips, mouth, ear canal, and/or pharynx.
