The 27-year-old, who appeared in NBC's drama American Dreams, apparently accompanied Hathaway to the New Orleans screening of her new film Rachel Getting Married.
According to Life & Style, Shulman said: "We met through mutual friends. I came to support Anne. We've never been to New Orleans before - it's our first time."
Last month, Hathaway revealed that she had found love, but remained tight-lipped as to the man's identity. It is her first romance since splitting from Raffaello Follieri, who was recently jailed for four-and-a-half years after being found guilty of fraud.
A source said: "Adam's everything Raffaello wasn't. He's sensitive and kind to a fault. I think Anne may have found a kindred spirit."