Northern Ireland's world number two is recovering from a stress fracture of his rib and had already withdrawn from next week's Dubai Desert Classic.
Four-time major winner McIlroy, 27, is in the early stages of rehabilitation and has been able to start putting.
His planned return comes just a month before the Masters.
He will aim to complete the career Grand Slam at Augusta, the one major he has yet to win.
McIlroy complained about back pain during this month's South Africa Open, at which he lost in a play-off to England's Graeme Storm.
He played in Johannesburg with his back taped up and having taken anti-inflammatory tablets.
Rory McIlroy will miss next month's Genesis Open and Honda Classic and hopes to make his comeback from injury at the WGC event in Mexico in March.