Minutes before the gates were scheduled to open at noon, fans began climbing over metal barricades and surged toward the entrance, according to local news reports.
Three people suffered minor leg injuries and were transported to area hospitals after being trampled, ABC affiliate KTRK-TV reported.
Scott, who founded and curates the festival, posted video of the chaotic scene on Instagram.
The footage showed attendees first climbing over the metal barriers, then a massive crowd knocked the gates down and ran toward the entrance.
Houston police told CBS affiliate KHOU-TV they were trying to get additional officers to the scene to control the crowd.
The lineup for this year’s one-day festival includes performances by Scott, Gucci Mane, Migos, Pharrell, Rosalia, the Houston All Stars and many others. More than 50,000 people were expected to attend.
Scott performed in the Super Bowl halftime show with Maroon 5 earlier this year, and in August Netflix began streaming the documentary, Travis Scott: Look Mom I Can Fly, taking viewers inside the Grammy-nominated rapper’s world.