The 30-year-old actor, wearing a basic red tee and jeans, was all smiles when leaving a local market with Cuoco who wore a printed top, skinny jeans and floppy hat, reported Aceshowbiz.
Their romance rumour came to surface after Cavill, 30, and Cuoco, 27, were spotted going on a hike, followed by a stop for sushi near her Sherman Oaks home.
"They were both single and started dating recently," a source had said. "Immortals" star Cavill previously dated "Fast and Furious 6" actress Gina Carano. They split in early May.
Photos: Sunny Deol with sons Karan and Rajvir at Mumbai airport
Photos: 10 beautiful moments that capture winter around the world
Muhammad Ali birth anniversary: Top boxing films of all time in pics
Photos: Karisma Kapoor, Preity Zinta, Shraddha Kapoor at Mumbai airport
Spotted: Anushka Sharma and Diljit Dosanjh at Mumbai studio