It is indeed Italian, but the musical ornamentation
and the apparently non-Italian pronunciation of the singer makes it actually difficult to parse, even for an Italian.
The text says:
Procuri pur ch'io sia
Esule dal tuo affetto e dal tuo core,
Che non farà ch'amore
Abbandoni già mai l'anima mia.
More or less (I don't know the context), it say that even if she is exiled from someone's affection and heart, nonetheless her love won't leave her soul.
It's a verse from the cantata “Usurpator tiranno della tua libertà”, on a text by an anonymous author and with music by Giovanni Felice Sances (1600?-1679). Here you can find the whole text (not always perfectly transcribed).