The broadcast nature of wireless channels and broad coverage brings significant challenges to the security of Satellite Internet. Recently, a new security paradigm named covert communication aims to enhance security by hiding the transmission process and has received great research attention. Various covert transmission schemes were proposed to achieve covertness for different network scenarios. Motivated by the importance of promising security techniques, this survey provides a comprehensive overview of the recent works on covert communication in Satellite Internet for the first time. We first introduce the basic architecture and characteristics of Satellite Internet, as well as its access security challenges. Then, an in-depth overview of covert communication technologies is provided with an emphasis, which is divided into two categories, i.e., traditional ones and information theory-based ones. Finally, several key challenges and future research directions on covert communication are presented.