"With Izumi, valuing her companionship, and aware of her feelings for him, Itachi opted to put Izumi under a powerful Tsukuyomi to allow her to live the life she'd always dreamed with him, allowing her death to be quick and peaceful."
"When the illusion ended, Izumi collapsed and used her final moment of consciousness to thank Itachi. She then died, the death she experienced within the illusion tricking her body into expiring as well." looks like Itachi inderectly killed her.
@Nicholas8293 he used the genjutsu on her but Tobi was the one who finished her off. So he indirectly killed her by letting Tobi kill her with his own hands.