Laudator Temporis Acti

Oxford English Dictionary (OED), s.v. havoc:

[a. AFr. havok, altered in some way from OF. havot (c1150 in Du Cange, havo), used in same sense, esp. in phrase crier havot. Prob. of Teutonic origin.]

Du Cange, Glossarium ad scriptores mediae et infimae Latinitatis, s.v. havo:

Odo de Diogilo lib. 4. de Ludovici VII. profect. in Orient. pag. 42: Veniunt de exercitu, qui cambiunt necessaria, junguntur et illis, qui ambiunt non sua. Igitur una die Flandrensis quidam dignus flagris et flamma, cernens immensas divitias, et immoderata cupiditate caecatus, clamat, Havo, Havo, rapiens, quod cupivit, etc. Flandris, Have, sunt divitiae, opes, pecuniae, etc. ex Lat. Habere. Sic clamabat ille: Quot bona, quot bona! ut alios ad praedam invitaret.

Du Cange is citing Odo of Deuil, De Ludovici VII profectione in Orientem, i.e. The Journey of Louis VII to the East, tr. Virginia Gingerick Berry:

From the army came people who were bartering for necessities, and they were joined by men who coveted the supplies of others. One day, therefore, a certain Fleming, fit to be scourged and burned in Hell, seeing the great wealth and blinded by immoderate greed, cried, "Havo! Havo!" seizing what he wished.

Anatoly Liberman, A Bibliography of English Etymology: Sources and Word List (Minneapolis: University of Minnesota Press, 2009), p. 621, s.v. havoc, cites:

Anonymous. 1889ii; Bernard, Thomas L. 1976; Grondhound, C. 1884: 354-5; J.C. 1877; Susenmihl, Ernst. 1855:329.

The names Grondhound and Susenmihl are incorrect. The first is a reference to C. Grondhoud, "Doublets in English, II" Taalstudie 5 (1884) 349-364 (at 354-355), and the second is a reference to Ernst Susemihl, "Zur Geschichte und Etymologie der englischen Sprache," Archiv für das Studium der neueren Sprachen und Literaturen 18 (1855) 321-43 (at 329). Grondhoud (with Trench and others before him) posited a connection between havoc and hawk, but I don't know if anyone today takes that theory seriously. See Walter W. Skeat, Notes on English Etymology, Chiefly Reprinted from the Transactions of the Philological Society (Oxford: Clarendon Press, 1901), pp. 128-129, for more speculation on the etymology of havoc.

The OED defines havoc as:

1. In the phrase cry havoc, orig. to give to an army the order havoc!, as the signal for the seizure of spoil, and so of general spoliation or pillage. In later use (usually after Shakes.) fig., and associated with sense 2.

2. Devastation, destruction; esp. in phr. to make havoc, play havoc (freq. const. with), in which the earlier sense of spoliation or plunder has gradually passed into that of destructive devastation. Also in weakened sense: confusion and disorder, disarray. The phrases to work havoc, create havoc are also common.

One can also wreak (but please not reek or wreck) havoc. See OED, s.v. wreak, sense 8.b.: "To cause or effect (harm, damage, etc.), esp. in phr. to wreak havoc."