The OED does not attest 'green-eyed' before Shakespeare, and a scan of the English Poetry and Verse Drama databases does not turn up evidence for "green-eyed jealousy" as a 16th century stock phrase. So the green-eyed monster of jealousy may owe its proverbial status at least in part to a Shakespearean coinage. But regardless of how conventional the association may have been, it is worth pointing out that the two Shakespearean occurrences of 'green-eyed' link The Merchant and Venice and Othello at strategic moments and establish jealousy as an important component of the relationship of the two plays.
In a famous passage Iago "warns" Othello only to entrap him more fully:
165 O, beware, my lord, of jealousy!
166
It is the green-ey'd monster which doth mock
167
The meat it feeds on. (Oth.
3.3.165-167)
When Bassanio chooses lead over gold and silver and concludes with the words "And here choose I. Joy be the consequence" Portia's aside can be read as a remarkably clairvoyant and accurate forecast of the stages of Othello's career, coupled with a prayer that Desdemona's fate not be hers. But Portia never prays without taking her own precautions, and her ability to retain circumspection at the point of ecstasy distinguishes her from her Venetian sister:
108 [Aside.] How all the other passions fleet
to air,
109
As doubtful thoughts, and rash-embrac'd despair,
110
And shudd'ring fear, and green-eyed jealousy!
111
O love, be moderate, allay thy ecstasy,
112
In measure rain thy joy, scant this excess!
113
I feel too much thy blessing; make it less.
(Mev.
3.2.108-113)
Structurally, this moment is not unlike Othello's arrival in Cyprus: the sailor/suitor encounters the beloved on the Island of Love. And one may profitably compare Portia's prophetic prayer with Othello's very different and unconsciously ironic prophetic vision:
O my soul's joy!
185 If after every tempest come such
calms,
186 May the winds blow till they have
waken'd death!
187 And let the laboring bark climb
hills of seas
188 Olympus-high, and duck again as
low
189 As hell's from heaven! If it were
now to die,
190 'Twere now to be most happy; for I
fear
191 My soul hath her content so
absolute
192 That not another comfort like to
this
193 Succeeds in unknown fate. (Oth.
2.1.184-193)