In continuation of the theme that you can’t trust any of today’s dictionaries to reliably summarize what’s known about the etymology of a word, consider how they summarize the etymology of MASSAGE:
Merriam-Webster @ M-W.com: French, from masser to massage, from Arabic massa to stroke. First Known Use in English: circa 1860
Webster’s New World @ YourDictionary.com: Fr < masser, to massage < Ar massa, to touch
American Heritage @ YourDictionary.com: French, from masser, to massage, from Arabic masaḥa, to stroke, anoint; see mšḥ in Semitic roots or massa, to touch; see mšš in Semitic roots.
Collins English @ Dictionary.com: Century19: from French, from masser to rub; see mass [NOTE: at ‘’mass’’, ‘’mass’’ is stated to be from Latin ‘’massa’’]
Chambers Dict @ ChambersHarrap.co.uk:: 19c: French, from masser to massage, from Greek massein to knead. [question: directly modern Greek? or ancient Greek along unspecified path?]
Concise OED @ OxfordDictionaries.com: late 19th century: from French, from masser ‘knead, treat with massage’, probably from Portuguese amassar ‘knead’, from massa ‘dough’
Random House @ Dictionary.com: 1875–80; < F, equiv. to mass ( er ) to massage (< Ar massa to handle) + -age
Notice the absence of uncertainty: The first three say French ‘’massage’’ is certainly directly from Arabic, the fourth says the French is certainly directly from Latin, the fifth says the French is certainly from Greek (modern? or ancient?), the sixth says the French is probably directly from a Portuguese root, and the seventh, if I interpret its notation correctly, says the French is probably directly from Arabic.
The official dictionary of the French language says the French verb ‘’masser’’ meaning to massage is first attested in French in 1779—ref: CNRTL.fr, sup2—and the noun ‘’massage’’ is first attested in French in 1808—ref: CNRTL.fr. This dictionary too says the French comes directly from Arabic ‘’massa’’ meaning to touch, and it adds the remark: “The fact that the [early French] word appeared chiefly in accounts of travels in the Orient [the Middle East] seems to preclude the hypothesis offered by some that it came from Greek.”
All the dictionaries above that go with the Arabic ‘’massa’’ proposition say correctly that in Arabic ‘’massa’’ meant to touch—not to massage. The practice of massage was common in the Middle East for centuries before it started to become common in the West in the mid-to-late 19th century. But the Arabic word for massage was not ‘’massa’’ or anything close to it. The fact that the early evidences of the French word appear chiefly in accounts of travels in the Middle East, and yet these did not use the Arabic word for massage, seems to preclude the hypothesis that it came from Arabic.
Leonhard Rauwolf visited the Middle East in 1573-75, and published a 300+ page narrative of his visit in 1582. He says that massage was very common (search his book for the string “ bath"), and he has a detailed description of massage and of the bath houses where the massage took place. His book in English translation is downloadable at Archive.org (a massage at a bathhouse in Lebanon in 1573 is described on pages 37-38 of the djVu electronic copy, which is pages 20-21 of the print). The Middle Eastern bathhouses entered Western Europe in the mid-to-late 19th century under the name “Turkish bath”. In the Europe of the later 19th century you could get a “massage” at a Turkish bathhouse. Before then, the word massage was confined to accounts in travelers in the Middle East plus some attestations in a medical context.
The Arabic word for massage is تمسيد ‘’tamsīd’’ (also تدليك ‘’tadlīk’’). This Arabic word تمسيد ‘’tamsīd’’ contains the rootword مس ‘’mas’’ meaning to touch, to physically feel (such as with your fingers). The Arabic مسحة ‘’masha’’ (pronounced mas-ha) is much the same thing as ‘’mas’’. The root ‘’mas’’ or ‘’mas-ha’’ is what the dictionaries quoted above are saying is the source for the French ‘’massage’’. But ‘’mas’’ and ‘’mas-ha’’ do not mean massage at all. They are not tamsīd! Here’s how one of today’s Arabic-English dictionary defines ‘’mas’’: [Verb]: befall, contact, feel, finger, graze, handle, impinge, palpate, tip, twiddle, touch. [Noun]: touch. Similary the dictionary defines ‘’mas-ha’’ as: [Noun]: trace, touch, bit, streak, smack, tang, suggestion, tinge, shade, tint, hue. Arabic also has the verb مسح ‘’mas-h’’ or ‘’masah’’ defined as [Verb]: wipe, mop, mop up, rub, clean, polish, sweep, sponge, swab, extinguish, scrub.
I can find no explanation of how the various French travelers in the Middle East took up that or one of those Arabic words, and turned it into French ‘’masser’’, bearing in mind that the Arabs themselves didn’t use the word in that sense. The dictionaries appear to be relying solely on the phonetic similarity between an Arabic ‘’massa’’ and French ‘’masser’’.