GoDaddy.com, the closely held website that registers Internet domain names, has put itself up for sale in an auction that could fetch more than $1 billion, people familiar with the matter said.

Qatalyst Partners, the boutique firm run by veteran technology banker Frank Quattrone, has been hired to shop the Go Daddy Group Inc., which runs the world's largest domain name registrar, these people said. Private-equity firms are expected to bid for the company, which currently has more than 43 million domains under...