Mimosa pudica is listed as a non-toxic plant for humans on the University of California's list of safe and poisonous garden plants. It is also listed as safe for humans and pets on the University of Connecticut College of Agriculture and Natural Resources website.
The plant may be sensitive to the touch, but when it comes to care, it isn't really all that sensitive. In fact, it is considered an invasive weed in many areas, including Hawaii. The plant grows best in full sun or partial shade, and in rich, moist soil. One thing it is sensitive to, however, is cold. Native to tropical America, it is not tolerant of frost and is hardy outdoors only in U.S. Department of Agriculture plant hardiness zones 9 through 12. For this reason, and because it is such a novelty, it is often grown as an indoor plant.
It's not just the motion of the sensitive plant that may make it attractive to cats. The plant is a showy one. The flowers look like purple or pink puffballs, and the fact that it is a low-lying plant makes it easy for little paws to reach. Sensitive plants can spread to 5 feet as they creep along the ground.
Just because the sensitive plant is nontoxic doesn't necessarily mean it is completely safe for cats. This is because if a cat consumes any plant -- even a non-toxic plant -- there is always a risk of stomachache or choking, according to the ASPCA. For this reason, if you suspect your cat has eaten part of the plant, contact your veterinarian as soon as possible.